Simplify (x^2-5x-24)/(6x+2x^2)*(5x^2)/(8-x)

$\frac{x^{2} - 5 x - 24}{6 x + 2 x^{2}} \cdot \frac{5 x^{2}}{8 - x}$

Step 1

Factor $x^{2} - 5 x - 24$ 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 $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$\frac{(x - 8) (x + 3)}{6 x + 2 x^{2}} \cdot \frac{5 x^{2}}{8 - x}$

Step 2

Simplify terms.

Factor $2 x$ out of $6 x + 2 x^{2}$ .

Factor $2 x$ out of $6 x$ .

$\frac{(x - 8) (x + 3)}{2 x (3) + 2 x^{2}} \cdot \frac{5 x^{2}}{8 - x}$

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

$\frac{(x - 8) (x + 3)}{2 x (3) + 2 x (x)} \cdot \frac{5 x^{2}}{8 - x}$

Factor $2 x$ out of $2 x (3) + 2 x (x)$ .

$\frac{(x - 8) (x + 3)}{2 x (3 + x)} \cdot \frac{5 x^{2}}{8 - x}$

Cancel the common factor of $x$ .

Factor $x$ out of $2 x (3 + x)$ .

$\frac{(x - 8) (x + 3)}{x (2 (3 + x))} \cdot \frac{5 x^{2}}{8 - x}$

Factor $x$ out of $5 x^{2}$ .

$\frac{(x - 8) (x + 3)}{x (2 (3 + x))} \cdot \frac{x (5 x)}{8 - x}$

Cancel the common factor.

$\frac{(x - 8) (x + 3)}{x (2 (3 + x))} \cdot \frac{x (5 x)}{8 - x}$

Rewrite the expression.

$\frac{(x - 8) (x + 3)}{2 (3 + x)} \cdot \frac{5 x}{8 - x}$

Multiply $\frac{(x - 8) (x + 3)}{2 (3 + x)}$ by $\frac{5 x}{8 - x}$ .

$\frac{(x - 8) (x + 3) (5 x)}{2 (3 + x) (8 - x)}$

Cancel the common factor of $x - 8$ and $8 - x$ .

Factor $- 1$ out of $x$ .

$\frac{(- 1 (- x) - 8) (x + 3) (5 x)}{2 (3 + x) (8 - x)}$

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{(- 1 (- x) - 1 (8)) (x + 3) (5 x)}{2 (3 + x) (8 - x)}$

Factor $- 1$ out of $- 1 (- x) - 1 (8)$ .

$\frac{- 1 (- x + 8) (x + 3) (5 x)}{2 (3 + x) (8 - x)}$

Reorder terms.

$\frac{- 1 (- x + 8) (x + 3) (5 x)}{2 (3 + x) (- x + 8)}$

Cancel the common factor.

$\frac{- 1 (- x + 8) (x + 3) (5 x)}{2 (3 + x) (- x + 8)}$

Rewrite the expression.

$\frac{(- 1 (x + 3)) (5 x)}{2 (3 + x)}$

Cancel the common factor of $x + 3$ and $3 + x$ .

Reorder terms.

$\frac{(- 1 (x + 3)) (5 x)}{2 (x + 3)}$

Cancel the common factor.

$\frac{- 1 (x + 3) (5 x)}{2 (x + 3)}$

Rewrite the expression.

$\frac{(- 1) (5 x)}{2}$

Simplify the expression.

Multiply $- 1$ by $5$ .

$\frac{- 5 x}{2}$

Move the negative in front of the fraction.

$- \frac{5 x}{2}$

Simplify (x^2-5x-24)/(6x+2x^2)*(5x^2)/(8-x)

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