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

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$b$

Step 3

Multiply each term in $\frac{a - b}{b} + c = a$ by $b$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a - b}{b} + c = a$ by $b$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $b$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$a - b + c b = a b$

Step 4

Solve the equation.

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Step 4.1

Subtract $a b$ from both sides of the equation.

$a - b + c b - a b = 0$

Step 4.2

Subtract $a$ from both sides of the equation.

$- b + c b - a b = - a$

Step 4.3

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

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Step 4.3.1

Factor $b$ out of $- b$ .

$b \cdot - 1 + c b - a b = - a$

Step 4.3.2

Factor $b$ out of $c b$ .

$b \cdot - 1 + b c - a b = - a$

Step 4.3.3

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

$b \cdot - 1 + b c + b (- a) = - a$

Step 4.3.4

Factor $b$ out of $b \cdot - 1 + b c$ .

$b \cdot (- 1 + c) + b (- a) = - a$

Step 4.3.5

Factor $b$ out of $b \cdot (- 1 + c) + b (- a)$ .

$b (- 1 + c - a) = - a$

Step 4.4

Divide each term in $b (- 1 + c - a) = - a$ by $- 1 + c - a$ and simplify.

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Step 4.4.1

Divide each term in $b (- 1 + c - a) = - a$ by $- 1 + c - a$ .

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $- 1 + c - a$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $b$ by $1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

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

Step 4.4.3.2

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 4.4.3.3

Factor $- 1$ out of $c$ .

$b = - \frac{a}{- 1 (1) - 1 (- c) - a}$

Step 4.4.3.4

Factor $- 1$ out of $- 1 (1) - 1 (- c)$ .

$b = - \frac{a}{- 1 (1 - c) - a}$

Step 4.4.3.5

Factor $- 1$ out of $- a$ .

$b = - \frac{a}{- 1 (1 - c) - (a)}$

Step 4.4.3.6

Factor $- 1$ out of $- 1 (1 - c) - (a)$ .

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

Step 4.4.3.7

Simplify the expression.

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Step 4.4.3.7.1

Move the negative in front of the fraction.

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

Step 4.4.3.7.2

Multiply $- 1$ by $- 1$ .

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

Step 4.4.3.7.3

Multiply $\frac{a}{1 - c + a}$ by $1$ .

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