Pre-Algebra Examples

$\frac{x^{2}}{x^{2} - 36} \cdot \frac{x^{2} - 11 z + 30}{x^{2} - 5 x}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2}}{x^{2} - 6^{2}} \cdot \frac{x^{2} - 11 z + 30}{x^{2} - 5 x}$

Step 1.2

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 $b = 6$ .

$\frac{x^{2}}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x^{2} - 5 x}$

Step 2

Simplify terms.

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Step 2.1

Factor $x$ out of $x^{2} - 5 x$ .

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Step 2.1.1

Factor $x$ out of $x^{2}$ .

$\frac{x^{2}}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x \cdot x - 5 x}$

Step 2.1.2

Factor $x$ out of $- 5 x$ .

$\frac{x^{2}}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x \cdot x + x \cdot - 5}$

Step 2.1.3

Factor $x$ out of $x \cdot x + x \cdot - 5$ .

$\frac{x^{2}}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x (x - 5)}$

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Factor $x$ out of $x^{2}$ .

$\frac{x \cdot x}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x (x - 5)}$

Step 2.2.2

Cancel the common factor.

$\frac{x \cdot x}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x (x - 5)}$

Step 2.2.3

Rewrite the expression.

$\frac{x}{(x + 6) (x - 6)} \cdot \frac{x^{2} - 11 z + 30}{x - 5}$

Step 2.3

Multiply $\frac{x}{(x + 6) (x - 6)}$ by $\frac{x^{2} - 11 z + 30}{x - 5}$ .

$\frac{x (x^{2} - 11 z + 30)}{(x + 6) (x - 6) (x - 5)}$