Simplify (x^3+2x^2-24x)/(x^2-14x+40)*(x^2-4x-60)/((x+6)^2)

$\frac{x^{3} + 2 x^{2} - 24 x}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

Simplify the numerator.

Factor $x$ out of $x^{3} + 2 x^{2} - 24 x$ .

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

$\frac{x \cdot x^{2} + 2 x^{2} - 24 x}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

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

$\frac{x \cdot x^{2} + x (2 x) - 24 x}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

Factor $x$ out of $- 24 x$ .

$\frac{x \cdot x^{2} + x (2 x) + x \cdot - 24}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

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

$\frac{x (x^{2} + 2 x) + x \cdot - 24}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

Factor $x$ out of $x (x^{2} + 2 x) + x \cdot - 24$ .

$\frac{x (x^{2} + 2 x - 24)}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

Factor $x^{2} + 2 x - 24$ 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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Write the factored form using these integers.

$\frac{x ((x - 4) (x + 6))}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

$\frac{x (x - 4) (x + 6)}{x^{2} - 14 x + 40} \cdot \frac{x^{2} - 4 x - 60}{{(x + 6)}^{2}}$

Factor $x^{2} - 14 x + 40$ 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 $40$ and whose sum is $- 14$ .

$- 10, - 4$

Write the factored form using these integers.

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

Factor $x^{2} - 4 x - 60$ 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 $- 60$ and whose sum is $- 4$ .

$- 10, 6$

Write the factored form using these integers.

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

Simplify terms.

Combine.

$\frac{x (x - 4) (x + 6) ((x - 10) (x + 6))}{(x - 10) (x - 4) {(x + 6)}^{2}}$

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{x (x - 4) (x + 6) ((x - 10) (x + 6))}{(x - 10) (x - 4) {(x + 6)}^{2}}$

Rewrite the expression.

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

Cancel the common factor of $x + 6$ and ${(x + 6)}^{2}$ .

Factor $x + 6$ out of $(x (x + 6)) ((x - 10) (x + 6))$ .

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

Cancel the common factors.

Factor $x + 6$ out of $(x - 10) {(x + 6)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 10$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$x$

Simplify (x^3+2x^2-24x)/(x^2-14x+40)*(x^2-4x-60)/((x+6)^2)

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