Simplify ((x^2+2x-24)/(x-3))÷((x+4)/(x-3))

$\frac{x^{2} + 2 x - 24}{x - 3} \div \frac{x + 4}{x - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + 2 x - 24}{x - 3} \cdot \frac{x - 3}{x + 4}$

Step 2

Simplify terms.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{x^{2} + 2 x - 24}{x - 3} \cdot \frac{x - 3}{x + 4}$

Rewrite the expression.

$(x^{2} + 2 x - 24) \frac{1}{x + 4}$

Multiply $x^{2} + 2 x - 24$ by $\frac{1}{x + 4}$ .

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

Step 3

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.

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

Simplify ((x^2+2x-24)/(x-3))÷((x+4)/(x-3))

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