Simplify ((x^2-9)(x^2-z^2))/(4(x+z)(x-3))

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

Step 1

Simplify the numerator.

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

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

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 $b = 3$ .

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

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.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + z$ .

Cancel the common factor.

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

Rewrite the expression.

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