Algebra Examples

$\frac{4}{x - y} - \frac{7}{y - x}$

Step 1

Factor $- 1$ out of $y$ .

$\frac{4}{x - y} - \frac{7}{- 1 (- y) - x}$

Step 2

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

$\frac{4}{x - y} - \frac{7}{- 1 (- y) - (x)}$

Step 3

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

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

Step 4

Reorder terms.

$\frac{4}{x - y} - \frac{7}{- 1 (x - y)}$

Step 5

To write $\frac{4}{x - y}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{4}{x - y} \cdot \frac{- 1}{- 1} - \frac{7}{- 1 (x - y)}$

Step 6

Write each expression with a common denominator of $(x - y) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

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

$\frac{4 \cdot - 1}{(x - y) \cdot - 1} - \frac{7}{- 1 (x - y)}$

Step 6.2

Reorder the factors of $(x - y) \cdot - 1$ .

$\frac{4 \cdot - 1}{- (x - y)} - \frac{7}{- 1 (x - y)}$

Step 7

Combine the numerators over the common denominator.

$\frac{4 \cdot - 1 - 7}{- (x - y)}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $4$ by $- 1$ .

$\frac{- 4 - 7}{- (x - y)}$

Step 8.2

Subtract $7$ from $- 4$ .

$\frac{- 11}{- (x - y)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{11}{x - y}$