Simplify (9x^2)/(x-6)(x^2-36)/(3x-6)3/(4x^2+24x)

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 36}{3 x - 6} \cdot \frac{3}{4 x^{2} + 24 x}$

Factor $4 x$ out of $4 x^{2} + 24 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 36}{3 x - 6} \cdot \frac{3}{4 x (x) + 24 x}$

Factor $4 x$ out of $24 x$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 36}{3 x - 6} \cdot \frac{3}{4 x (x) + 4 x (6)}$

Factor $4 x$ out of $4 x (x) + 4 x (6)$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 36}{3 x - 6} \cdot \frac{3}{4 x (x + 6)}$

Simplify the numerator.

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

$\frac{9 x^{2}}{x - 6} \cdot \frac{x^{2} - 6^{2}}{3 x - 6} \cdot \frac{3}{4 x (x + 6)}$

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 $b = 6$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 x - 6} \cdot \frac{3}{4 x (x + 6)}$

Simplify terms.

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 (x) - 6} \cdot \frac{3}{4 x (x + 6)}$

Factor $3$ out of $- 6$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 x + 3 \cdot - 2} \cdot \frac{3}{4 x (x + 6)}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{9 x^{2}}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 (x - 2)} \cdot \frac{3}{4 x (x + 6)}$

Cancel the common factor of $3$ .

Factor $3$ out of $9 x^{2}$ .

$\frac{3 (3 x^{2})}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 (x - 2)} \cdot \frac{3}{4 x (x + 6)}$

Cancel the common factor.

$\frac{3 (3 x^{2})}{x - 6} \cdot \frac{(x + 6) (x - 6)}{3 (x - 2)} \cdot \frac{3}{4 x (x + 6)}$

Rewrite the expression.

$\frac{3 x^{2}}{x - 6} \cdot \frac{(x + 6) (x - 6)}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Cancel the common factor of $x - 6$ .

Factor $x - 6$ out of $(x + 6) (x - 6)$ .

$\frac{3 x^{2}}{x - 6} \cdot \frac{(x - 6) (x + 6)}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Cancel the common factor.

$\frac{3 x^{2}}{x - 6} \cdot \frac{(x - 6) (x + 6)}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Rewrite the expression.

$3 x^{2} \cdot \frac{x + 6}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Combine $3$ and $\frac{x + 6}{x - 2}$ .

$x^{2} \cdot \frac{3 (x + 6)}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Combine $x^{2}$ and $\frac{3 (x + 6)}{x - 2}$ .

$\frac{x^{2} (3 (x + 6))}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Cancel the common factor of $x (x + 6)$ .

Factor $x (x + 6)$ out of $x^{2} \cdot 3 (x + 6)$ .

$\frac{x (x + 6) (x \cdot 3)}{x - 2} \cdot \frac{3}{4 x (x + 6)}$

Factor $x (x + 6)$ out of $4 x (x + 6)$ .

$\frac{x (x + 6) (x \cdot 3)}{x - 2} \cdot \frac{3}{x (x + 6) (4)}$

Cancel the common factor.

$\frac{x (x + 6) (x \cdot 3)}{x - 2} \cdot \frac{3}{x (x + 6) \cdot 4}$

Rewrite the expression.

$\frac{x \cdot 3}{x - 2} \cdot \frac{3}{4}$

Multiply $\frac{x \cdot 3}{x - 2}$ by $\frac{3}{4}$ .

$\frac{x \cdot 3 \cdot 3}{(x - 2) \cdot 4}$

Simplify the expression.

Multiply $3$ by $3$ .

$\frac{x \cdot 9}{(x - 2) \cdot 4}$

Move $9$ to the left of $x$ .

$\frac{9 \cdot x}{(x - 2) \cdot 4}$

Move $4$ to the left of $x - 2$ .

$\frac{9 x}{4 (x - 2)}$

Simplify (9x^2)/(x-6)*(x^2-36)/(3x-6)*3/(4x^2+24x)

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Simplify (9x^2)/(x-6)(x^2-36)/(3x-6)3/(4x^2+24x)