Pre-Algebra Examples

$\frac{x^{2} - 4}{64 x} \div \frac{2 - x}{8 x y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 4}{64 x} \cdot \frac{8 x y}{2 - x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $8 x$ .

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Step 2.1.1

Factor $8 x$ out of $64 x$ .

$\frac{x^{2} - 4}{8 x (8)} \cdot \frac{8 x y}{2 - x}$

Step 2.1.2

Factor $8 x$ out of $8 x y$ .

$\frac{x^{2} - 4}{8 x (8)} \cdot \frac{8 x (y)}{2 - x}$

Step 2.1.3

Cancel the common factor.

$\frac{x^{2} - 4}{8 x \cdot 8} \cdot \frac{8 x y}{2 - x}$

Step 2.1.4

Rewrite the expression.

$\frac{x^{2} - 4}{8} \cdot \frac{y}{2 - x}$

Step 2.2

Multiply $\frac{x^{2} - 4}{8}$ by $\frac{y}{2 - x}$ .

$\frac{(x^{2} - 4) y}{8 (2 - x)}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Step 4

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

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Step 4.1

Factor $- 1$ out of $x$ .

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

Step 4.2

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 4.3

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

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

Step 4.4

Reorder terms.

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

Step 4.5

Cancel the common factor.

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

Step 4.6

Rewrite the expression.

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

Step 5

Factor out negative.

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

Step 6

Move the negative in front of the fraction.

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

Step 7

Reorder factors in $- \frac{(x + 2) y}{8}$ .

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