Algebra Examples

$a = \frac{a - b}{b} + c$

Step 1

Rewrite the equation as $\frac{a - b}{b} + c = a$ .

$\frac{a - b}{b} + c = a$

Step 2

Simplify $\frac{a - b}{b} + c$ .

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Step 2.1

To write $c$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{a - b}{b} + \frac{c b}{b} = a$

Step 2.2

Combine the numerators over the common denominator.

$\frac{a - b + c b}{b} = a$

Step 3

Multiply both sides by $b$ .

$\frac{a - b + c b}{b} b = a b$

Step 4

Simplify the left side.

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Step 4.1

Simplify $\frac{a - b + c b}{b} b$ .

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Step 4.1.1

Cancel the common factor of $b$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{a - b + c b}{b} b = a b$

Step 4.1.1.2

Rewrite the expression.

$a - b + c b = a b$

Step 4.1.2

Simplify the expression.

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Step 4.1.2.1

Reorder $c$ and $b$ .

$a - b + b c = a b$

Step 4.1.2.2

Move $- b$ .

$a + b c - b = a b$

Step 4.1.2.3

Reorder $a$ and $b c$ .

$b c + a - b = a b$

Step 5

Solve for $c$ .

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Step 5.1

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

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Step 5.1.1

Subtract $a$ from both sides of the equation.

$b c - b = a b - a$

Step 5.1.2

Add $b$ to both sides of the equation.

$b c = a b - a + b$

Step 5.2

Divide each term in $b c = a b - a + b$ by $b$ and simplify.

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Step 5.2.1

Divide each term in $b c = a b - a + b$ by $b$ .

$\frac{b c}{b} = \frac{a b}{b} + \frac{- a}{b} + \frac{b}{b}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $b$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{b c}{b} = \frac{a b}{b} + \frac{- a}{b} + \frac{b}{b}$

Step 5.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{a b}{b} + \frac{- a}{b} + \frac{b}{b}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Simplify each term.

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Step 5.2.3.1.1

Cancel the common factor of $b$ .

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Step 5.2.3.1.1.1

Cancel the common factor.

$c = \frac{a b}{b} + \frac{- a}{b} + \frac{b}{b}$

Step 5.2.3.1.1.2

Divide $a$ by $1$ .

$c = a + \frac{- a}{b} + \frac{b}{b}$

Step 5.2.3.1.2

Move the negative in front of the fraction.

$c = a - \frac{a}{b} + \frac{b}{b}$

Step 5.2.3.1.3

Cancel the common factor of $b$ .

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Step 5.2.3.1.3.1

Cancel the common factor.

$c = a - \frac{a}{b} + \frac{b}{b}$

Step 5.2.3.1.3.2

Rewrite the expression.

$c = a - \frac{a}{b} + 1$