Algebra Examples

$\frac{x + 2}{2 x + 7} \div \frac{x^{4}}{x - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 2}{2 x + 7} \cdot \frac{x - 2}{x^{4}}$

Step 2

Multiply $\frac{x + 2}{2 x + 7}$ by $\frac{x - 2}{x^{4}}$ .

$\frac{(x + 2) (x - 2)}{(2 x + 7) x^{4}}$

Step 3

Reorder factors in $\frac{(x + 2) (x - 2)}{(2 x + 7) x^{4}}$ .

$\frac{(x + 2) (x - 2)}{x^{4} (2 x + 7)}$

Step 4

Expand $(x + 2) (x - 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$\frac{x (x - 2) + 2 (x - 2)}{x^{4} (2 x + 7)}$

Step 4.2

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 2 + 2 (x - 2)}{x^{4} (2 x + 7)}$

Step 4.3

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2}{x^{4} (2 x + 7)}$

Step 5

Combine the opposite terms in $x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$ .

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Step 5.1

Reorder the factors in the terms $x \cdot - 2$ and $2 x$ .

$\frac{x \cdot x - 2 x + 2 x + 2 \cdot - 2}{x^{4} (2 x + 7)}$

Step 5.2

Add $- 2 x$ and $2 x$ .

$\frac{x \cdot x + 0 + 2 \cdot - 2}{x^{4} (2 x + 7)}$

Step 5.3

Add $x \cdot x$ and $0$ .

$\frac{x \cdot x + 2 \cdot - 2}{x^{4} (2 x + 7)}$

Step 6

Simplify each term.

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Step 6.1

Multiply $x$ by $x$ .

$\frac{x^{2} + 2 \cdot - 2}{x^{4} (2 x + 7)}$

Step 6.2

Multiply $2$ by $- 2$ .

$\frac{x^{2} - 4}{x^{4} (2 x + 7)}$

Step 7

Split the fraction $\frac{x^{2} - 4}{x^{4} (2 x + 7)}$ into two fractions.

$\frac{x^{2}}{x^{4} (2 x + 7)} + \frac{- 4}{x^{4} (2 x + 7)}$

Step 8

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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Step 8.1

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{x^{4} (2 x + 7)} + \frac{- 4}{x^{4} (2 x + 7)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $x^{2}$ out of $x^{4} (2 x + 7)$ .

$\frac{x^{2} \cdot 1}{x^{2} (x^{2} (2 x + 7))} + \frac{- 4}{x^{4} (2 x + 7)}$

Step 8.2.2

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (x^{2} (2 x + 7))} + \frac{- 4}{x^{4} (2 x + 7)}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{x^{2} (2 x + 7)} + \frac{- 4}{x^{4} (2 x + 7)}$

Step 9

Move the negative in front of the fraction.

$\frac{1}{x^{2} (2 x + 7)} - \frac{4}{x^{4} (2 x + 7)}$