Algebra Examples

$A = \sqrt{s (s - a) (s - b) (s - c)}$

Step 1

Rewrite the equation as $\sqrt{s (s - a) (s - b) (s - c)} = A$ .

$\sqrt{s (s - a) (s - b) (s - c)} = A$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{s (s - a) (s - b) (s - c)}}^{2} = A^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{s (s - a) (s - b) (s - c)}$ as ${(s (s - a) (s - b) (s - c))}^{\frac{1}{2}}$ .

${({(s (s - a) (s - b) (s - c))}^{\frac{1}{2}})}^{2} = A^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(s (s - a) (s - b) (s - c))}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Simplify by multiplying through.

Tap for more steps...

Step 3.2.1.1.1

Multiply the exponents in ${({(s (s - a) (s - b) (s - c))}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(s (s - a) (s - b) (s - c))}^{\frac{1}{2} \cdot 2} = A^{2}$

Step 3.2.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.1.2.1

Cancel the common factor.

${(s (s - a) (s - b) (s - c))}^{\frac{1}{2} \cdot 2} = A^{2}$

Step 3.2.1.1.1.2.2

Rewrite the expression.

${(s (s - a) (s - b) (s - c))}^{1} = A^{2}$

Step 3.2.1.1.2

Apply the distributive property.

${((s \cdot s + s (- a)) (s - b) (s - c))}^{1} = A^{2}$

Step 3.2.1.1.3

Simplify the expression.

Tap for more steps...

Step 3.2.1.1.3.1

Multiply $s$ by $s$ .

${((s^{2} + s (- a)) (s - b) (s - c))}^{1} = A^{2}$

Step 3.2.1.1.3.2

Rewrite using the commutative property of multiplication.

${((s^{2} - s a) (s - b) (s - c))}^{1} = A^{2}$

Step 3.2.1.2

Expand $(s^{2} - s a) (s - b)$ using the FOIL Method.

Tap for more steps...

Step 3.2.1.2.1

Apply the distributive property.

${((s^{2} (s - b) - s a (s - b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.2.2

Apply the distributive property.

${((s^{2} s + s^{2} (- b) - s a (s - b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.2.3

Apply the distributive property.

${((s^{2} s + s^{2} (- b) - s a s - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3

Simplify each term.

Tap for more steps...

Step 3.2.1.3.1

Multiply $s^{2}$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.3.1.1

Multiply $s^{2}$ by $s$ .

Tap for more steps...

Step 3.2.1.3.1.1.1

Raise $s$ to the power of $1$ .

${((s^{2} s^{1} + s^{2} (- b) - s a s - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${((s^{2 + 1} + s^{2} (- b) - s a s - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.1.2

Add $2$ and $1$ .

${((s^{3} + s^{2} (- b) - s a s - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.2

Rewrite using the commutative property of multiplication.

${((s^{3} - s^{2} b - s a s - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.3

Multiply $s$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.3.3.1

Move $s$ .

${((s^{3} - s^{2} b - (s \cdot s) a - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.3.2

Multiply $s$ by $s$ .

${((s^{3} - s^{2} b - s^{2} a - s a (- b)) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.4

Multiply $- s a (- b)$ .

Tap for more steps...

Step 3.2.1.3.4.1

Multiply $- 1$ by $- 1$ .

${((s^{3} - s^{2} b - s^{2} a + 1 s a b) (s - c))}^{1} = A^{2}$

Step 3.2.1.3.4.2

Multiply $s$ by $1$ .

${((s^{3} - s^{2} b - s^{2} a + s a b) (s - c))}^{1} = A^{2}$

Step 3.2.1.4

Expand $(s^{3} - s^{2} b - s^{2} a + s a b) (s - c)$ by multiplying each term in the first expression by each term in the second expression.

${(s^{3} s + s^{3} (- c) - s^{2} b s - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5

Simplify terms.

Tap for more steps...

Step 3.2.1.5.1

Simplify each term.

Tap for more steps...

Step 3.2.1.5.1.1

Multiply $s^{3}$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.5.1.1.1

Multiply $s^{3}$ by $s$ .

Tap for more steps...

Step 3.2.1.5.1.1.1.1

Raise $s$ to the power of $1$ .

${(s^{3} s^{1} + s^{3} (- c) - s^{2} b s - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(s^{3 + 1} + s^{3} (- c) - s^{2} b s - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.1.2

Add $3$ and $1$ .

${(s^{4} + s^{3} (- c) - s^{2} b s - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.2

Rewrite using the commutative property of multiplication.

${(s^{4} - s^{3} c - s^{2} b s - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.3

Multiply $s^{2}$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.5.1.3.1

Move $s$ .

${(s^{4} - s^{3} c - (s \cdot s^{2}) b - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.3.2

Multiply $s$ by $s^{2}$ .

Tap for more steps...

Step 3.2.1.5.1.3.2.1

Raise $s$ to the power of $1$ .

${(s^{4} - s^{3} c - (s^{1} s^{2}) b - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(s^{4} - s^{3} c - s^{1 + 2} b - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.3.3

Add $1$ and $2$ .

${(s^{4} - s^{3} c - s^{3} b - s^{2} b (- c) - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.4

Multiply $- s^{2} b (- c)$ .

Tap for more steps...

Step 3.2.1.5.1.4.1

Multiply $- 1$ by $- 1$ .

${(s^{4} - s^{3} c - s^{3} b + 1 s^{2} b c - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.4.2

Multiply $s^{2}$ by $1$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{2} a s - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.5

Multiply $s^{2}$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.5.1.5.1

Move $s$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - (s \cdot s^{2}) a - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.5.2

Multiply $s$ by $s^{2}$ .

Tap for more steps...

Step 3.2.1.5.1.5.2.1

Raise $s$ to the power of $1$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - (s^{1} s^{2}) a - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{1 + 2} a - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.5.3

Add $1$ and $2$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a - s^{2} a (- c) + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.6

Multiply $- s^{2} a (- c)$ .

Tap for more steps...

Step 3.2.1.5.1.6.1

Multiply $- 1$ by $- 1$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + 1 s^{2} a c + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.6.2

Multiply $s^{2}$ by $1$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s a b s + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.7

Multiply $s$ by $s$ by adding the exponents.

Tap for more steps...

Step 3.2.1.5.1.7.1

Move $s$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s \cdot s a b + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.7.2

Multiply $s$ by $s$ .

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s^{2} a b + s a b (- c))}^{1} = A^{2}$

Step 3.2.1.5.1.8

Rewrite using the commutative property of multiplication.

${(s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s^{2} a b - s a b c)}^{1} = A^{2}$

Step 3.2.1.5.2

Simplify.

$s^{4} - s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s^{2} a b - s a b c = A^{2}$

Step 4

Solve for $c$ .

Tap for more steps...

Step 4.1

Move all terms not containing $c$ to the right side of the equation.

Tap for more steps...

Step 4.1.1

Subtract $s^{4}$ from both sides of the equation.

$- s^{3} c - s^{3} b + s^{2} b c - s^{3} a + s^{2} a c + s^{2} a b - s a b c = A^{2} - s^{4}$

Step 4.1.2

Add $s^{3} b$ to both sides of the equation.

$- s^{3} c + s^{2} b c - s^{3} a + s^{2} a c + s^{2} a b - s a b c = A^{2} - s^{4} + s^{3} b$

Step 4.1.3

Add $s^{3} a$ to both sides of the equation.

$- s^{3} c + s^{2} b c + s^{2} a c + s^{2} a b - s a b c = A^{2} - s^{4} + s^{3} b + s^{3} a$

Step 4.1.4

Subtract $s^{2} a b$ from both sides of the equation.

$- s^{3} c + s^{2} b c + s^{2} a c - s a b c = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2

Factor $s c$ out of $- s^{3} c + s^{2} b c + s^{2} a c - s a b c$ .

Tap for more steps...

Step 4.2.1

Factor $s c$ out of $- s^{3} c$ .

$s c (- s^{2}) + s^{2} b c + s^{2} a c - s a b c = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.2

Factor $s c$ out of $s^{2} b c$ .

$s c (- s^{2}) + s c (s b) + s^{2} a c - s a b c = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.3

Factor $s c$ out of $s^{2} a c$ .

$s c (- s^{2}) + s c (s b) + s c (s a) - s a b c = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.4

Factor $s c$ out of $- s a b c$ .

$s c (- s^{2}) + s c (s b) + s c (s a) + s c (- 1 a b) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.5

Factor $s c$ out of $s c (- s^{2}) + s c (s b)$ .

$s c (- s^{2} + s b) + s c (s a) + s c (- 1 a b) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.6

Factor $s c$ out of $s c (- s^{2} + s b) + s c (s a)$ .

$s c (- s^{2} + s b + s a) + s c (- 1 a b) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.2.7

Factor $s c$ out of $s c (- s^{2} + s b + s a) + s c (- 1 a b)$ .

$s c (- s^{2} + s b + s a - 1 a b) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.3

Factor out the greatest common factor from each group.

Tap for more steps...

Step 4.3.1

Group the first two terms and the last two terms.

$s c ((- s^{2} + s b) + s a - 1 a b) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.3.2

Factor out the greatest common factor (GCF) from each group.

$s c (s (- s + b) - a (- s + b)) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.4

Factor.

Tap for more steps...

Step 4.4.1

Factor the polynomial by factoring out the greatest common factor, $- s + b$ .

$s c ((- s + b) (s - a)) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.4.2

Remove unnecessary parentheses.

$s c (- s + b) (s - a) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$

Step 4.5

Divide each term in $s c (- s + b) (s - a) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$ by $s (- s + b) (s - a)$ and simplify.

Tap for more steps...

Step 4.5.1

Divide each term in $s c (- s + b) (s - a) = A^{2} - s^{4} + s^{3} b + s^{3} a - s^{2} a b$ by $s (- s + b) (s - a)$ .

$\frac{s c (- s + b) (s - a)}{s (- s + b) (s - a)} = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.2

Simplify the left side.

Tap for more steps...

Step 4.5.2.1

Cancel the common factor of $s$ .

Tap for more steps...

Step 4.5.2.1.1

Cancel the common factor.

Step 4.5.2.1.2

Rewrite the expression.

$\frac{(c (- s + b)) (s - a)}{(- s + b) (s - a)} = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.2.2

Cancel the common factor of $- s + b$ .

Tap for more steps...

Step 4.5.2.2.1

Cancel the common factor.

$\frac{c (- s + b) (s - a)}{(- s + b) (s - a)} = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.2.2.2

Rewrite the expression.

$\frac{(c) (s - a)}{s - a} = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.2.3

Cancel the common factor of $s - a$ .

Tap for more steps...

Step 4.5.2.3.1

Cancel the common factor.

$\frac{c (s - a)}{s - a} = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.2.3.2

Divide $c$ by $1$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{4}}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3

Simplify the right side.

Tap for more steps...

Step 4.5.3.1

Simplify each term.

Tap for more steps...

Step 4.5.3.1.1

Cancel the common factor of $s^{4}$ and $s$ .

Tap for more steps...

Step 4.5.3.1.1.1

Factor $s$ out of $- s^{4}$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{s (- s^{3})}{s (- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.1.2.1

Factor $s$ out of $s (- s + b) (s - a)$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{s (- s^{3})}{s ((- s + b) (s - a))} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.1.2.2

Cancel the common factor.

Step 4.5.3.1.1.2.3

Rewrite the expression.

$c = \frac{A^{2}}{s (- s + b) (s - a)} + \frac{- s^{3}}{(- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.2

Move the negative in front of the fraction.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{3} b}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.3

Cancel the common factor of $s^{3}$ and $s$ .

Tap for more steps...

Step 4.5.3.1.3.1

Factor $s$ out of $s^{3} b$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s (s^{2} b)}{s (- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.3.2.1

Factor $s$ out of $s (- s + b) (s - a)$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s (s^{2} b)}{s ((- s + b) (s - a))} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.3.2.2

Cancel the common factor.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s (s^{2} b)}{s ((- s + b) (s - a))} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.3.2.3

Rewrite the expression.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{3} a}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.4

Cancel the common factor of $s^{3}$ and $s$ .

Tap for more steps...

Step 4.5.3.1.4.1

Factor $s$ out of $s^{3} a$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s (s^{2} a)}{s (- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.4.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.4.2.1

Factor $s$ out of $s (- s + b) (s - a)$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s (s^{2} a)}{s ((- s + b) (s - a))} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.4.2.2

Cancel the common factor.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s (s^{2} a)}{s ((- s + b) (s - a))} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.4.2.3

Rewrite the expression.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} + \frac{- s^{2} a b}{s (- s + b) (s - a)}$

Step 4.5.3.1.5

Cancel the common factor of $s^{2}$ and $s$ .

Tap for more steps...

Step 4.5.3.1.5.1

Factor $s$ out of $- s^{2} a b$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} + \frac{s (- s a b)}{s (- s + b) (s - a)}$

Step 4.5.3.1.5.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.5.2.1

Factor $s$ out of $s (- s + b) (s - a)$ .

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} + \frac{s (- s a b)}{s ((- s + b) (s - a))}$

Step 4.5.3.1.5.2.2

Cancel the common factor.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} + \frac{s (- s a b)}{s ((- s + b) (s - a))}$

Step 4.5.3.1.5.2.3

Rewrite the expression.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} + \frac{- s a b}{(- s + b) (s - a)}$

Step 4.5.3.1.6

Move the negative in front of the fraction.

$c = \frac{A^{2}}{s (- s + b) (s - a)} - \frac{s^{3}}{(- s + b) (s - a)} + \frac{s^{2} b}{(- s + b) (s - a)} + \frac{s^{2} a}{(- s + b) (s - a)} - \frac{s a b}{(- s + b) (s - a)}$