Trigonometry Examples

$\frac{9 x}{2 y - 3 x} - \frac{5 y}{3 x - 2 y}$

Step 1

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

$\frac{9 x}{2 y - 3 x} - \frac{5 y}{- (- 3 x) - 2 y}$

Step 2

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

$\frac{9 x}{2 y - 3 x} - \frac{5 y}{- (- 3 x) - (2 y)}$

Step 3

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

$\frac{9 x}{2 y - 3 x} - \frac{5 y}{- (- 3 x + 2 y)}$

Step 4

Reorder terms.

$\frac{9 x}{- 3 x + 2 y} - \frac{5 y}{- (- 3 x + 2 y)}$

Step 5

To write $\frac{9 x}{- 3 x + 2 y}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{9 x}{- 3 x + 2 y} \cdot \frac{- 1}{- 1} - \frac{5 y}{- (- 3 x + 2 y)}$

Step 6

Write each expression with a common denominator of $(- 3 x + 2 y) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.1

Multiply $\frac{9 x}{- 3 x + 2 y}$ by $\frac{- 1}{- 1}$ .

$\frac{9 x \cdot - 1}{(- 3 x + 2 y) \cdot - 1} - \frac{5 y}{- (- 3 x + 2 y)}$

Step 6.2

Reorder the factors of $(- 3 x + 2 y) \cdot - 1$ .

$\frac{9 x \cdot - 1}{- (- 3 x + 2 y)} - \frac{5 y}{- (- 3 x + 2 y)}$

Step 7

Combine the numerators over the common denominator.

$\frac{9 x \cdot - 1 - 5 y}{- (- 3 x + 2 y)}$

Step 8

Simplify the expression.

Tap for more steps...

Step 8.1

Multiply $- 1$ by $9$ .

$\frac{- 9 x - 5 y}{- (- 3 x + 2 y)}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{- 9 x - 5 y}{- 3 x + 2 y}$

Step 9

Factor $- 1$ out of $- 9 x$ .

$- \frac{- (9 x) - 5 y}{- 3 x + 2 y}$

Step 10

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

$- \frac{- (9 x) - (5 y)}{- 3 x + 2 y}$

Step 11

Factor $- 1$ out of $- (9 x) - (5 y)$ .

$- \frac{- (9 x + 5 y)}{- 3 x + 2 y}$

Step 12

Rewrite $- (9 x + 5 y)$ as $- 1 (9 x + 5 y)$ .

$- \frac{- 1 (9 x + 5 y)}{- 3 x + 2 y}$

Step 13

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

$- \frac{- 1 (9 x + 5 y)}{- (3 x) + 2 y}$

Step 14

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

$- \frac{- 1 (9 x + 5 y)}{- (3 x) - (- 2 y)}$

Step 15

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

$- \frac{- 1 (9 x + 5 y)}{- (3 x - 2 y)}$

Step 16

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

$- \frac{- 1 (9 x + 5 y)}{- 1 (3 x - 2 y)}$

Step 17

Cancel the common factor.

$- \frac{- 1 (9 x + 5 y)}{- 1 (3 x - 2 y)}$

Step 18

Rewrite the expression.

$- \frac{9 x + 5 y}{3 x - 2 y}$