Simplify (5x)/(x-6)+1/(6-x)

$\frac{5 x}{x - 6} + \frac{1}{6 - x}$

Step 1

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{5 x}{x - 6} + \frac{1}{- 1 (- 6) - x}$

Step 2

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

$\frac{5 x}{x - 6} + \frac{1}{- 1 (- 6) - (x)}$

Step 3

Factor $- 1$ out of $- 1 (- 6) - (x)$ .

$\frac{5 x}{x - 6} + \frac{1}{- 1 (- 6 + x)}$

Step 4

Simplify the expression.

Move a negative from the denominator of $\frac{1}{- 1 (- 6 + x)}$ to the numerator.

$\frac{5 x}{x - 6} + \frac{- 1 \cdot 1}{- 6 + x}$

Reorder terms.

$\frac{5 x}{x - 6} + \frac{- 1 \cdot 1}{x - 6}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 x - 1 \cdot 1}{x - 6}$

Step 6

Multiply $- 1$ by $1$ .

$\frac{5 x - 1}{x - 6}$