Simplify ((x-8)/(10x^3+70x^2))÷(1/(x+7))

$\frac{x - 8}{10 x^{3} + 70 x^{2}} \div \frac{1}{x + 7}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 8}{10 x^{3} + 70 x^{2}} (x + 7)$

Step 2

Factor $10 x^{2}$ out of $10 x^{3} + 70 x^{2}$ .

Factor $10 x^{2}$ out of $10 x^{3}$ .

$\frac{x - 8}{10 x^{2} (x) + 70 x^{2}} (x + 7)$

Factor $10 x^{2}$ out of $70 x^{2}$ .

$\frac{x - 8}{10 x^{2} (x) + 10 x^{2} (7)} (x + 7)$

Factor $10 x^{2}$ out of $10 x^{2} (x) + 10 x^{2} (7)$ .

$\frac{x - 8}{10 x^{2} (x + 7)} (x + 7)$

Step 3

Cancel the common factor of $x + 7$ .

Factor $x + 7$ out of $10 x^{2} (x + 7)$ .

$\frac{x - 8}{(x + 7) (10 x^{2})} (x + 7)$

Cancel the common factor.

$\frac{x - 8}{(x + 7) (10 x^{2})} (x + 7)$

Rewrite the expression.

$\frac{x - 8}{10 x^{2}}$