Simplify (5x)/(x-2)-7/(2-x)

$\frac{5 x}{x - 2} - \frac{7}{2 - x}$

Step 1

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

$\frac{5 x}{x - 2} - \frac{7}{- 1 (- 2) - x}$

Step 2

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

$\frac{5 x}{x - 2} - \frac{7}{- 1 (- 2) - (x)}$

Step 3

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

$\frac{5 x}{x - 2} - \frac{7}{- 1 (- 2 + x)}$

Step 4

Reorder terms.

$\frac{5 x}{x - 2} - \frac{7}{- 1 (x - 2)}$

Step 5

To write $\frac{5 x}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{5 x}{x - 2} \cdot \frac{- 1}{- 1} - \frac{7}{- 1 (x - 2)}$

Step 6

Write each expression with a common denominator of $(x - 2) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{x - 2}$ by $\frac{- 1}{- 1}$ .

$\frac{5 x \cdot - 1}{(x - 2) \cdot - 1} - \frac{7}{- 1 (x - 2)}$

Reorder the factors of $(x - 2) \cdot - 1$ .

$\frac{5 x \cdot - 1}{- (x - 2)} - \frac{7}{- 1 (x - 2)}$

Step 7

Combine the numerators over the common denominator.

$\frac{5 x \cdot - 1 - 7}{- (x - 2)}$

Step 8

Simplify the expression.

Multiply $- 1$ by $5$ .

$\frac{- 5 x - 7}{- (x - 2)}$

Move the negative in front of the fraction.

$- \frac{- 5 x - 7}{x - 2}$

Step 9

Factor $- 1$ out of $- 5 x$ .

$- \frac{- (5 x) - 7}{x - 2}$

Step 10

Rewrite $- 7$ as $- 1 (7)$ .

$- \frac{- (5 x) - 1 (7)}{x - 2}$

Step 11

Factor $- 1$ out of $- (5 x) - 1 (7)$ .

$- \frac{- (5 x + 7)}{x - 2}$

Step 12

Simplify the expression.

Rewrite $- (5 x + 7)$ as $- 1 (5 x + 7)$ .

$- \frac{- 1 (5 x + 7)}{x - 2}$

Move the negative in front of the fraction.

$- - \frac{5 x + 7}{x - 2}$

Multiply $- 1$ by $- 1$ .

$1 \frac{5 x + 7}{x - 2}$

Multiply $\frac{5 x + 7}{x - 2}$ by $1$ .

$\frac{5 x + 7}{x - 2}$

Simplify (5x)/(x-2)-7/(2-x)

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