Simplify (20x-15)/(-10x+15)

$\frac{20 x - 15}{- 10 x + 15}$

Step 1

Cancel the common factor of $20 x - 15$ and $- 10 x + 15$ .

Factor $5$ out of $20 x$ .

$\frac{5 (4 x) - 15}{- 10 x + 15}$

Factor $5$ out of $- 15$ .

$\frac{5 (4 x) + 5 (- 3)}{- 10 x + 15}$

Factor $5$ out of $5 (4 x) + 5 (- 3)$ .

$\frac{5 (4 x - 3)}{- 10 x + 15}$

Cancel the common factors.

Factor $5$ out of $- 10 x$ .

$\frac{5 (4 x - 3)}{5 (- 2 x) + 15}$

Factor $5$ out of $15$ .

$\frac{5 (4 x - 3)}{5 (- 2 x) + 5 (3)}$

Factor $5$ out of $5 (- 2 x) + 5 (3)$ .

$\frac{5 (4 x - 3)}{5 (- 2 x + 3)}$

Cancel the common factor.

$\frac{5 (4 x - 3)}{5 (- 2 x + 3)}$

Rewrite the expression.

$\frac{4 x - 3}{- 2 x + 3}$

$\frac{4 x - 3}{- 2 x + 3}$

$\frac{4 x - 3}{- 2 x + 3}$

Step 2

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

$\frac{4 x - 3}{- (2 x) + 3}$

Step 3

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

$\frac{4 x - 3}{- (2 x) - 1 (- 3)}$

Step 4

Factor $- 1$ out of $- (2 x) - 1 (- 3)$ .

$\frac{4 x - 3}{- (2 x - 3)}$

Step 5

Rewrite negatives.

Rewrite $- (2 x - 3)$ as $- 1 (2 x - 3)$ .

$\frac{4 x - 3}{- 1 (2 x - 3)}$

Move the negative in front of the fraction.

$- \frac{4 x - 3}{2 x - 3}$

$- \frac{4 x - 3}{2 x - 3}$

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