Precalculus Examples

$\frac{3}{x - 2} + \frac{5}{2 - x}$

Step 1

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

$\frac{3}{x - 2} + \frac{5}{- 1 (- 2) - x}$

Step 2

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

$\frac{3}{x - 2} + \frac{5}{- 1 (- 2) - (x)}$

Step 3

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

$\frac{3}{x - 2} + \frac{5}{- 1 (- 2 + x)}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Move a negative from the denominator of $\frac{5}{- 1 (- 2 + x)}$ to the numerator.

$\frac{3}{x - 2} + \frac{- 1 \cdot 5}{- 2 + x}$

Step 4.2

Reorder terms.

$\frac{3}{x - 2} + \frac{- 1 \cdot 5}{x - 2}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 - 1 \cdot 5}{x - 2}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $- 1$ by $5$ .

$\frac{3 - 5}{x - 2}$

Step 6.2

Subtract $5$ from $3$ .

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

Step 7

Move the negative in front of the fraction.

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