Algebra Examples

$\frac{x - 4}{2 x^{2}} \div \frac{2 x + 3}{x + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 4}{2 x^{2}} \cdot \frac{x + 4}{2 x + 3}$

Step 2

Multiply $\frac{x - 4}{2 x^{2}}$ by $\frac{x + 4}{2 x + 3}$ .

$\frac{(x - 4) (x + 4)}{2 x^{2} (2 x + 3)}$

Step 3

Expand $(x - 4) (x + 4)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$\frac{x (x + 4) - 4 (x + 4)}{2 x^{2} (2 x + 3)}$

Step 3.2

Apply the distributive property.

$\frac{x \cdot x + x \cdot 4 - 4 (x + 4)}{2 x^{2} (2 x + 3)}$

Step 3.3

Apply the distributive property.

$\frac{x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Step 4

Combine the opposite terms in $x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4$ .

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Step 4.1

Reorder the factors in the terms $x \cdot 4$ and $- 4 x$ .

$\frac{x \cdot x + 4 x - 4 x - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Step 4.2

Subtract $4 x$ from $4 x$ .

$\frac{x \cdot x + 0 - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Step 4.3

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

$\frac{x \cdot x - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Step 5

Simplify each term.

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Step 5.1

Multiply $x$ by $x$ .

$\frac{x^{2} - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Step 5.2

Multiply $- 4$ by $4$ .

$\frac{x^{2} - 16}{2 x^{2} (2 x + 3)}$

Step 6

Split the fraction $\frac{x^{2} - 16}{2 x^{2} (2 x + 3)}$ into two fractions.

$\frac{x^{2}}{2 x^{2} (2 x + 3)} + \frac{- 16}{2 x^{2} (2 x + 3)}$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{x^{2}}{2 x^{2} (2 x + 3)} + \frac{- 16}{2 x^{2} (2 x + 3)}$

Step 7.2

Rewrite the expression.

$\frac{1}{2 (2 x + 3)} + \frac{- 16}{2 x^{2} (2 x + 3)}$

Step 8

Cancel the common factor of $- 16$ and $2$ .

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Step 8.1

Factor $2$ out of $- 16$ .

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 x^{2} (2 x + 3)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2 x^{2} (2 x + 3)$ .

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 (x^{2} (2 x + 3))}$

Step 8.2.2

Cancel the common factor.

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 (x^{2} (2 x + 3))}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{2 (2 x + 3)} + \frac{- 8}{x^{2} (2 x + 3)}$

Step 9

Move the negative in front of the fraction.

$\frac{1}{2 (2 x + 3)} - \frac{8}{x^{2} (2 x + 3)}$