Pre-Algebra Examples

$\frac{\frac{a^{2} - b^{2}}{4 a}}{\frac{a + b}{2 a}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{a^{2} - b^{2}}{4 a} \cdot \frac{2 a}{a + b}$

Step 2

Cancel the common factor of $2 a$ .

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Step 2.1

Factor $2 a$ out of $4 a$ .

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

Step 2.2

Cancel the common factor.

$\frac{a^{2} - b^{2}}{2 a \cdot 2} \cdot \frac{2 a}{a + b}$

Step 2.3

Rewrite the expression.

$\frac{a^{2} - b^{2}}{2} \cdot \frac{1}{a + b}$

Step 3

Multiply $\frac{a^{2} - b^{2}}{2}$ by $\frac{1}{a + b}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 5

Cancel the common factor of $a + b$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{a - b}{2}$

Step 6

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

$\frac{a}{2} + \frac{- b}{2}$

Step 7

Move the negative in front of the fraction.

$\frac{a}{2} - \frac{b}{2}$