Simplify (5x+2)/(x-3)-2/(3-x)

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

Step 1

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 2

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

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

Step 3

Factor $- 1$ out of $- 1 (- 3) - (x)$ .

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

Step 4

Reorder terms.

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

Step 5

To write $\frac{5 x + 2}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

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

Step 6

Write each expression with a common denominator of $(x - 3) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x + 2}{x - 3}$ by $\frac{- 1}{- 1}$ .

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

Reorder the factors of $(x - 3) \cdot - 1$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 1$ by $5$ .

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

Multiply $2$ by $- 1$ .

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

Subtract $2$ from $- 2$ .

$\frac{- 5 x - 4}{- (x - 3)}$

Step 9

Simplify with factoring out.

Move the negative in front of the fraction.

$- \frac{- 5 x - 4}{x - 3}$

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

$- \frac{- (5 x) - 4}{x - 3}$

Rewrite $- 4$ as $- 1 (4)$ .

$- \frac{- (5 x) - 1 (4)}{x - 3}$

Factor $- 1$ out of $- (5 x) - 1 (4)$ .

$- \frac{- (5 x + 4)}{x - 3}$

Simplify the expression.

Rewrite $- (5 x + 4)$ as $- 1 (5 x + 4)$ .

$- \frac{- 1 (5 x + 4)}{x - 3}$

Move the negative in front of the fraction.

$- - \frac{5 x + 4}{x - 3}$

Multiply $- 1$ by $- 1$ .

$1 \frac{5 x + 4}{x - 3}$

Multiply $\frac{5 x + 4}{x - 3}$ by $1$ .

$\frac{5 x + 4}{x - 3}$

Simplify (5x+2)/(x-3)-2/(3-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.