Pre-Algebra Examples

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

Step 1

Factor $- 1$ out of $x$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

Reorder terms.

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Multiply $- 1$ by $5$ .

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

Step 7

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

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

Step 8

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

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

Step 9

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

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

Step 10

Rewrite negatives.

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Step 10.1

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

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

Step 10.2

Move the negative in front of the fraction.

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