Simplify ((x^2-7x-18)/(x+1))÷((x^2+2x)/(x+1))

$\frac{x^{2} - 7 x - 18}{x + 1} \div \frac{x^{2} + 2 x}{x + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 7 x - 18}{x + 1} \cdot \frac{x + 1}{x^{2} + 2 x}$

Step 2

Simplify terms.

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{x^{2} - 7 x - 18}{x + 1} \cdot \frac{x + 1}{x^{2} + 2 x}$

Rewrite the expression.

$(x^{2} - 7 x - 18) \frac{1}{x^{2} + 2 x}$

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

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

$(x^{2} - 7 x - 18) \frac{1}{x \cdot x + 2 x}$

Factor $x$ out of $2 x$ .

$(x^{2} - 7 x - 18) \frac{1}{x \cdot x + x \cdot 2}$

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$(x^{2} - 7 x - 18) \frac{1}{x (x + 2)}$

Multiply $x^{2} - 7 x - 18$ by $\frac{1}{x (x + 2)}$ .

$\frac{x^{2} - 7 x - 18}{x (x + 2)}$

Step 3

Factor $x^{2} - 7 x - 18$ 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 $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Write the factored form using these integers.

$\frac{(x - 9) (x + 2)}{x (x + 2)}$

Step 4

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x - 9) (x + 2)}{x (x + 2)}$

Rewrite the expression.

$\frac{x - 9}{x}$

Simplify ((x^2-7x-18)/(x+1))÷((x^2+2x)/(x+1))

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