Algebra Examples

$\frac{(x^{2} - 9) (x^{2} - z^{2})}{4 (x + z) (x - 3)}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{(x^{2} - 3^{2}) (x^{2} - z^{2})}{4 (x + z) (x - 3)}$

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 $b = 3$ .

$\frac{(x + 3) (x - 3) (x^{2} - z^{2})}{4 (x + z) (x - 3)}$

Step 1.3

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 $b = z$ .

$\frac{(x + 3) (x - 3) (x + z) (x - z)}{4 (x + z) (x - 3)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x - 3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(x + 3) (x - 3) (x + z) (x - z)}{4 (x + z) (x - 3)}$

Step 2.1.2

Rewrite the expression.

$\frac{((x + 3) (x + z)) (x - z)}{4 (x + z)}$

Step 2.2

Cancel the common factor of $x + z$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(x + 3) (x + z) (x - z)}{4 (x + z)}$

Step 2.2.2

Rewrite the expression.

$\frac{(x + 3) (x - z)}{4}$