Simplify (9x^3+36x^2-288x)/(6x^4-60x^3)*(x^2-9x-10)/(x^2+9x+8)

$\frac{9 x^{3} + 36 x^{2} - 288 x}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Simplify the numerator.

Factor $9 x$ out of $9 x^{3} + 36 x^{2} - 288 x$ .

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

$\frac{9 x (x^{2}) + 36 x^{2} - 288 x}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $9 x$ out of $36 x^{2}$ .

$\frac{9 x (x^{2}) + 9 x (4 x) - 288 x}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $9 x$ out of $- 288 x$ .

$\frac{9 x (x^{2}) + 9 x (4 x) + 9 x (- 32)}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $9 x$ out of $9 x (x^{2}) + 9 x (4 x)$ .

$\frac{9 x (x^{2} + 4 x) + 9 x (- 32)}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $9 x$ out of $9 x (x^{2} + 4 x) + 9 x (- 32)$ .

$\frac{9 x (x^{2} + 4 x - 32)}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $x^{2} + 4 x - 32$ 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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Write the factored form using these integers.

$\frac{9 x ((x - 4) (x + 8))}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

$\frac{9 x (x - 4) (x + 8)}{6 x^{4} - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $6 x^{3}$ out of $6 x^{4} - 60 x^{3}$ .

Factor $6 x^{3}$ out of $6 x^{4}$ .

$\frac{9 x (x - 4) (x + 8)}{6 x^{3} (x) - 60 x^{3}} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $6 x^{3}$ out of $- 60 x^{3}$ .

$\frac{9 x (x - 4) (x + 8)}{6 x^{3} (x) + 6 x^{3} (- 10)} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $6 x^{3}$ out of $6 x^{3} (x) + 6 x^{3} (- 10)$ .

$\frac{9 x (x - 4) (x + 8)}{6 x^{3} (x - 10)} \cdot \frac{x^{2} - 9 x - 10}{x^{2} + 9 x + 8}$

Factor $x^{2} - 9 x - 10$ 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 $- 10$ and whose sum is $- 9$ .

$- 10, 1$

Write the factored form using these integers.

$\frac{9 x (x - 4) (x + 8)}{6 x^{3} (x - 10)} \cdot \frac{(x - 10) (x + 1)}{x^{2} + 9 x + 8}$

Factor $x^{2} + 9 x + 8$ 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 $8$ and whose sum is $9$ .

$1, 8$

Write the factored form using these integers.

$\frac{9 x (x - 4) (x + 8)}{6 x^{3} (x - 10)} \cdot \frac{(x - 10) (x + 1)}{(x + 1) (x + 8)}$

Simplify terms.

Combine.

$\frac{9 x (x - 4) (x + 8) ((x - 10) (x + 1))}{6 x^{3} (x - 10) ((x + 1) (x + 8))}$

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9 x (x - 4) (x + 8) ((x - 10) (x + 1))$ .

$\frac{3 (3 x (x - 4) (x + 8) ((x - 10) (x + 1)))}{6 x^{3} (x - 10) ((x + 1) (x + 8))}$

Cancel the common factors.

Factor $3$ out of $6 x^{3} (x - 10) ((x + 1) (x + 8))$ .

$\frac{3 (3 x (x - 4) (x + 8) ((x - 10) (x + 1)))}{3 (2 x^{3} (x - 10) ((x + 1) (x + 8)))}$

Cancel the common factor.

$\frac{3 (3 x (x - 4) (x + 8) ((x - 10) (x + 1)))}{3 (2 x^{3} (x - 10) ((x + 1) (x + 8)))}$

Rewrite the expression.

$\frac{3 x (x - 4) (x + 8) ((x - 10) (x + 1))}{2 x^{3} (x - 10) ((x + 1) (x + 8))}$

Cancel the common factor of $x$ and $x^{3}$ .

Factor $x$ out of $3 x (x - 4) (x + 8) ((x - 10) (x + 1))$ .

$\frac{x (((3 (x - 4)) (x + 8)) ((x - 10) (x + 1)))}{2 x^{3} (x - 10) ((x + 1) (x + 8))}$

Cancel the common factors.

Factor $x$ out of $2 x^{3} (x - 10) ((x + 1) (x + 8))$ .

$\frac{x (((3 (x - 4)) (x + 8)) ((x - 10) (x + 1)))}{x (2 x^{2} (x - 10) ((x + 1) (x + 8)))}$

Cancel the common factor.

$\frac{x (((3 (x - 4)) (x + 8)) ((x - 10) (x + 1)))}{x (2 x^{2} (x - 10) ((x + 1) (x + 8)))}$

Rewrite the expression.

$\frac{((3 (x - 4)) (x + 8)) ((x - 10) (x + 1))}{2 x^{2} (x - 10) ((x + 1) (x + 8))}$

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{3 (x - 4) (x + 8) ((x - 10) (x + 1))}{2 x^{2} (x - 10) ((x + 1) (x + 8))}$

Rewrite the expression.

$\frac{(3 (x - 4)) ((x - 10) (x + 1))}{2 x^{2} (x - 10) (x + 1)}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{3 (x - 4) ((x - 10) (x + 1))}{2 x^{2} (x - 10) (x + 1)}$

Rewrite the expression.

$\frac{(3 (x - 4)) (x + 1)}{2 x^{2} (x + 1)}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{3 (x - 4) (x + 1)}{2 x^{2} (x + 1)}$

Rewrite the expression.

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

Simplify (9x^3+36x^2-288x)/(6x^4-60x^3)*(x^2-9x-10)/(x^2+9x+8)

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