Algebra Examples

$\frac{a - b}{a + b} \div \frac{b}{a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a - b}{a + b} \cdot \frac{a}{b}$

Step 2

Multiply $\frac{a - b}{a + b}$ by $\frac{a}{b}$ .

$\frac{(a - b) a}{(a + b) b}$

Step 3

Reorder factors in $\frac{(a - b) a}{(a + b) b}$ .

$\frac{a (a - b)}{b (a + b)}$

Step 4

Apply the distributive property.

$\frac{a \cdot a + a (- b)}{b (a + b)}$

Step 5

Multiply $a$ by $a$ .

$\frac{a^{2} + a (- b)}{b (a + b)}$

Step 6

Rewrite using the commutative property of multiplication.

$\frac{a^{2} - a b}{b (a + b)}$

Step 7

Split the fraction $\frac{a^{2} - a b}{b (a + b)}$ into two fractions.

$\frac{a^{2}}{b (a + b)} + \frac{- a b}{b (a + b)}$

Step 8

Cancel the common factor of $b$ .

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Step 8.1

Cancel the common factor.

$\frac{a^{2}}{b (a + b)} + \frac{- a b}{b (a + b)}$

Step 8.2

Rewrite the expression.

$\frac{a^{2}}{b (a + b)} + \frac{- a}{a + b}$

Step 9

Move the negative in front of the fraction.

$\frac{a^{2}}{b (a + b)} - \frac{a}{a + b}$