Simplify (5x)/(7x-y)+4/(y-7x)

$\frac{5 x}{7 x - y} + \frac{4}{y - 7 x}$

Step 1

Factor $- 1$ out of $y$ .

$\frac{5 x}{7 x - y} + \frac{4}{- 1 (- y) - 7 x}$

Step 2

Factor $- 1$ out of $- 7 x$ .

$\frac{5 x}{7 x - y} + \frac{4}{- 1 (- y) - (7 x)}$

Step 3

Factor $- 1$ out of $- 1 (- y) - (7 x)$ .

$\frac{5 x}{7 x - y} + \frac{4}{- 1 (- y + 7 x)}$

Step 4

Simplify the expression.

Move a negative from the denominator of $\frac{4}{- 1 (- y + 7 x)}$ to the numerator.

$\frac{5 x}{7 x - y} + \frac{- 1 \cdot 4}{- y + 7 x}$

Reorder terms.

$\frac{5 x}{7 x - y} + \frac{- 1 \cdot 4}{7 x - y}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 x - 1 \cdot 4}{7 x - y}$

Step 6

Multiply $- 1$ by $4$ .

$\frac{5 x - 4}{7 x - y}$