Simplify (x^2+4x)/(x^2-2x-24)

$\frac{x^{2} + 4 x}{x^{2} - 2 x - 24}$

Step 1

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

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

$\frac{x \cdot x + 4 x}{x^{2} - 2 x - 24}$

Factor $x$ out of $4 x$ .

$\frac{x \cdot x + x \cdot 4}{x^{2} - 2 x - 24}$

Factor $x$ out of $x \cdot x + x \cdot 4$ .

$\frac{x (x + 4)}{x^{2} - 2 x - 24}$

Step 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 $- 2$ .

$- 6, 4$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{x - 6}$

Simplify (x^2+4x)/(x^2-2x-24)

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