Algebra Examples

$\frac{- \frac{y}{4} + \frac{4}{x}}{\frac{2 y}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

To write $- \frac{y}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 3

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{y}{4}$ by $\frac{x}{x}$ .

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

Step 4.2

Multiply $\frac{4}{x}$ by $\frac{4}{4}$ .

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

Step 4.3

Reorder the factors of $x \cdot 4$ .

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

Step 5

Combine the numerators over the common denominator.

$\frac{- y x + 4 \cdot 4}{4 x} \cdot \frac{x}{2 y}$

Step 6

Multiply $4$ by $4$ .

$\frac{- y x + 16}{4 x} \cdot \frac{x}{2 y}$

Step 7

Cancel the common factor of $x$ .

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Step 7.1

Factor $x$ out of $4 x$ .

$\frac{- y x + 16}{x \cdot 4} \cdot \frac{x}{2 y}$

Step 7.2

Cancel the common factor.

$\frac{- y x + 16}{x \cdot 4} \cdot \frac{x}{2 y}$

Step 7.3

Rewrite the expression.

$\frac{- y x + 16}{4} \cdot \frac{1}{2 y}$

Step 8

Multiply $\frac{- y x + 16}{4}$ by $\frac{1}{2 y}$ .

$\frac{- y x + 16}{4 (2 y)}$

Step 9

Multiply $2$ by $4$ .

$\frac{- y x + 16}{8 y}$

Step 10

Factor $- 1$ out of $- y x$ .

$\frac{- (y x) + 16}{8 y}$

Step 11

Rewrite $16$ as $- 1 (- 16)$ .

$\frac{- (y x) - 1 (- 16)}{8 y}$

Step 12

Factor $- 1$ out of $- (y x) - 1 (- 16)$ .

$\frac{- (y x - 16)}{8 y}$

Step 13

Simplify the expression.

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Step 13.1

Rewrite $- (y x - 16)$ as $- 1 (y x - 16)$ .

$\frac{- 1 (y x - 16)}{8 y}$

Step 13.2

Move the negative in front of the fraction.

$- \frac{y x - 16}{8 y}$