Simplify (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30)

$\frac{6 x - 60}{x^{3} + 3 x^{2}} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

Simplify with factoring out.

Factor $6$ out of $6 x - 60$ .

Factor $6$ out of $6 x$ .

$\frac{6 (x) - 60}{x^{3} + 3 x^{2}} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

Factor $6$ out of $- 60$ .

$\frac{6 x + 6 \cdot - 10}{x^{3} + 3 x^{2}} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

Factor $6$ out of $6 x + 6 \cdot - 10$ .

$\frac{6 (x - 10)}{x^{3} + 3 x^{2}} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

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

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

$\frac{6 (x - 10)}{x^{2} x + 3 x^{2}} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

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

$\frac{6 (x - 10)}{x^{2} x + x^{2} \cdot 3} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

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

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x^{3} - 9 x}{x^{2} - 13 x + 30}$

Simplify the numerator.

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

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

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x \cdot x^{2} - 9 x}{x^{2} - 13 x + 30}$

Factor $x$ out of $- 9 x$ .

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x \cdot x^{2} + x \cdot - 9}{x^{2} - 13 x + 30}$

Factor $x$ out of $x \cdot x^{2} + x \cdot - 9$ .

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x (x^{2} - 9)}{x^{2} - 13 x + 30}$

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

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x (x^{2} - 3^{2})}{x^{2} - 13 x + 30}$

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 $b = 3$ .

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x (x + 3) (x - 3)}{x^{2} - 13 x + 30}$

Factor $x^{2} - 13 x + 30$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $30$ and whose sum is $- 13$ .

$- 10, - 3$

Write the factored form using these integers.

$\frac{6 (x - 10)}{x^{2} (x + 3)} \cdot \frac{x (x + 3) (x - 3)}{(x - 10) (x - 3)}$

Simplify terms.

Combine.

$\frac{6 (x - 10) (x (x + 3) (x - 3))}{x^{2} (x + 3) ((x - 10) (x - 3))}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{6 (x - 10) (x (x + 3) (x - 3))}{x^{2} (x + 3) ((x - 10) (x - 3))}$

Rewrite the expression.

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $6 (x (x + 3) (x - 3))$ .

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

Cancel the common factors.

Factor $x$ out of $x^{2} (x + 3) (x - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{6 (x - 3)}{(x) (x - 3)}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{6 (x - 3)}{x (x - 3)}$

Rewrite the expression.

$\frac{6}{x}$

Simplify (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30)

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