Algebra Examples

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

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 $10 x^{3} + 70 x^{2}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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 $x + 7$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Split the fraction $\frac{x - 8}{10 x^{2}}$ into two fractions.

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

Step 5

Cancel the common factor of $x$ and $x^{2}$ .

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Step 5.1

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

$\frac{x^{1}}{10 x^{2}} + \frac{- 8}{10 x^{2}}$

Step 5.2

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

$\frac{x \cdot 1}{10 x^{2}} + \frac{- 8}{10 x^{2}}$

Step 5.3

Cancel the common factors.

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Step 5.3.1

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

$\frac{x \cdot 1}{x (10 x)} + \frac{- 8}{10 x^{2}}$

Step 5.3.2

Cancel the common factor.

$\frac{x \cdot 1}{x (10 x)} + \frac{- 8}{10 x^{2}}$

Step 5.3.3

Rewrite the expression.

$\frac{1}{10 x} + \frac{- 8}{10 x^{2}}$

Step 6

Cancel the common factor of $- 8$ and $10$ .

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Step 6.1

Factor $2$ out of $- 8$ .

$\frac{1}{10 x} + \frac{2 (- 4)}{10 x^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{1}{10 x} + \frac{2 (- 4)}{2 (5 x^{2})}$

Step 6.2.2

Cancel the common factor.

$\frac{1}{10 x} + \frac{2 \cdot - 4}{2 (5 x^{2})}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{10 x} + \frac{- 4}{5 x^{2}}$

Step 7

Move the negative in front of the fraction.

$\frac{1}{10 x} - \frac{4}{5 x^{2}}$