Simplify (x^3-3x^2-28x)/(15x^4-240x^3+945x^2)*(x-9)/(x+4)

$\frac{x^{3} - 3 x^{2} - 28 x}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Step 1

Simplify the numerator.

Factor $x$ out of $x^{3} - 3 x^{2} - 28 x$ .

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

$\frac{x \cdot x^{2} - 3 x^{2} - 28 x}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

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

$\frac{x \cdot x^{2} + x (- 3 x) - 28 x}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Factor $x$ out of $- 28 x$ .

$\frac{x \cdot x^{2} + x (- 3 x) + x \cdot - 28}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

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

$\frac{x (x^{2} - 3 x) + x \cdot - 28}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Factor $x$ out of $x (x^{2} - 3 x) + x \cdot - 28$ .

$\frac{x (x^{2} - 3 x - 28)}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Factor $x^{2} - 3 x - 28$ 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 $- 28$ and whose sum is $- 3$ .

$- 7, 4$

Write the factored form using these integers.

$\frac{x ((x - 7) (x + 4))}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

$\frac{x (x - 7) (x + 4)}{15 x^{4} - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Step 2

Simplify the denominator.

Factor $15 x^{2}$ out of $15 x^{4} - 240 x^{3} + 945 x^{2}$ .

Factor $15 x^{2}$ out of $15 x^{4}$ .

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x^{2}) - 240 x^{3} + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Factor $15 x^{2}$ out of $- 240 x^{3}$ .

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x^{2}) + 15 x^{2} (- 16 x) + 945 x^{2}} \cdot \frac{x - 9}{x + 4}$

Factor $15 x^{2}$ out of $945 x^{2}$ .

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x^{2}) + 15 x^{2} (- 16 x) + 15 x^{2} (63)} \cdot \frac{x - 9}{x + 4}$

Factor $15 x^{2}$ out of $15 x^{2} (x^{2}) + 15 x^{2} (- 16 x)$ .

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x^{2} - 16 x) + 15 x^{2} (63)} \cdot \frac{x - 9}{x + 4}$

Factor $15 x^{2}$ out of $15 x^{2} (x^{2} - 16 x) + 15 x^{2} (63)$ .

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x^{2} - 16 x + 63)} \cdot \frac{x - 9}{x + 4}$

Factor $x^{2} - 16 x + 63$ 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 $63$ and whose sum is $- 16$ .

$- 9, - 7$

Write the factored form using these integers.

$\frac{x (x - 7) (x + 4)}{15 x^{2} ((x - 9) (x - 7))} \cdot \frac{x - 9}{x + 4}$

$\frac{x (x - 7) (x + 4)}{15 x^{2} (x - 9) (x - 7)} \cdot \frac{x - 9}{x + 4}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $x (x - 7) (x + 4)$ .

$\frac{(x + 4) (x (x - 7))}{15 x^{2} (x - 9) (x - 7)} \cdot \frac{x - 9}{x + 4}$

Cancel the common factor.

$\frac{(x + 4) (x (x - 7))}{15 x^{2} (x - 9) (x - 7)} \cdot \frac{x - 9}{x + 4}$

Rewrite the expression.

$\frac{x (x - 7)}{15 x^{2} (x - 9) (x - 7)} \cdot (x - 9)$

Cancel the common factor of $x - 9$ .

Factor $x - 9$ out of $15 x^{2} (x - 9) (x - 7)$ .

$\frac{x (x - 7)}{(x - 9) (15 x^{2} (x - 7))} \cdot (x - 9)$

Cancel the common factor.

$\frac{x (x - 7)}{(x - 9) (15 x^{2} (x - 7))} \cdot (x - 9)$

Rewrite the expression.

$\frac{x (x - 7)}{15 x^{2} (x - 7)}$

Step 4

Cancel the common factors.

Factor $x$ out of $15 x^{2} (x - 7)$ .

$\frac{x (x - 7)}{x (15 x (x - 7))}$

Cancel the common factor.

$\frac{x (x - 7)}{x (15 x (x - 7))}$

Rewrite the expression.

$\frac{x - 7}{15 x (x - 7)}$

Step 5

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{x - 7}{15 x (x - 7)}$

Rewrite the expression.

$\frac{1}{15 x}$

Simplify (x^3-3x^2-28x)/(15x^4-240x^3+945x^2)*(x-9)/(x+4)

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