Simplify ((x^2+x)/(x^2-7x-8))÷((x^2)/(x^2-8x))

$\frac{x^{2} + x}{x^{2} - 7 x - 8} \div \frac{x^{2}}{x^{2} - 8 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + x}{x^{2} - 7 x - 8} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Step 2

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

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

$\frac{x \cdot x + x}{x^{2} - 7 x - 8} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Raise $x$ to the power of $1$ .

$\frac{x \cdot x + x^{1}}{x^{2} - 7 x - 8} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot x + x \cdot 1}{x^{2} - 7 x - 8} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Factor $x$ out of $x \cdot x + x \cdot 1$ .

$\frac{x (x + 1)}{x^{2} - 7 x - 8} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Step 3

Factor $x^{2} - 7 x - 8$ 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 $- 8$ and whose sum is $- 7$ .

$- 8, 1$

Write the factored form using these integers.

$\frac{x (x + 1)}{(x - 8) (x + 1)} \cdot \frac{x^{2} - 8 x}{x^{2}}$

Step 4

Simplify terms.

Cancel the common factor of $x$ .

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

$\frac{x (x + 1)}{(x - 8) (x + 1)} \cdot \frac{x^{2} - 8 x}{x \cdot x}$

Cancel the common factor.

$\frac{x (x + 1)}{(x - 8) (x + 1)} \cdot \frac{x^{2} - 8 x}{x \cdot x}$

Rewrite the expression.

$\frac{x + 1}{(x - 8) (x + 1)} \cdot \frac{x^{2} - 8 x}{x}$

Multiply $\frac{x + 1}{(x - 8) (x + 1)}$ by $\frac{x^{2} - 8 x}{x}$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{2} - 8 x}{(x - 8) x}$

Factor $x$ out of $x^{2} - 8 x$ .

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

$\frac{x \cdot x - 8 x}{(x - 8) x}$

Factor $x$ out of $- 8 x$ .

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

Factor $x$ out of $x \cdot x + x \cdot - 8$ .

$\frac{x (x - 8)}{(x - 8) x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (x - 8)}{(x - 8) x}$

Rewrite the expression.

$\frac{x - 8}{x - 8}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{x - 8}{x - 8}$

Rewrite the expression.

$1$

Simplify ((x^2+x)/(x^2-7x-8))÷((x^2)/(x^2-8x))

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