Pre-Algebra Examples

$(x^{2} - 25) \div \frac{(x - 3) (x + 5)}{x^{2} + 9}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(x^{2} - 25) \frac{x^{2} + 9}{(x - 3) (x + 5)}$

Step 2

Multiply $x^{2} - 25$ by $\frac{x^{2} + 9}{(x - 3) (x + 5)}$ .

$\frac{(x^{2} - 25) (x^{2} + 9)}{(x - 3) (x + 5)}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$\frac{(x^{2} - 5^{2}) (x^{2} + 9)}{(x - 3) (x + 5)}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{(x + 5) (x - 5) (x^{2} + 9)}{(x - 3) (x + 5)}$

Step 4

Cancel the common factor of $x + 5$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 5) (x - 5) (x^{2} + 9)}{(x - 3) (x + 5)}$

Step 4.2

Rewrite the expression.

$\frac{(x - 5) (x^{2} + 9)}{x - 3}$