Simplify a/(2a-b)+(3a-b)/(b-2a)

$\frac{a}{2 a - b} + \frac{(3 a - b)}{b - 2 a}$

Simplify terms.

Factor $- 1$ out of $b$ .

$\frac{a}{2 a - b} + \frac{3 a - b}{- 1 (- b) - 2 a}$

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

$\frac{a}{2 a - b} + \frac{3 a - b}{- 1 (- b) - (2 a)}$

Factor $- 1$ out of $- 1 (- b) - (2 a)$ .

$\frac{a}{2 a - b} + \frac{3 a - b}{- 1 (- b + 2 a)}$

Simplify the expression.

Move a negative from the denominator of $\frac{3 a - b}{- 1 (- b + 2 a)}$ to the numerator.

$\frac{a}{2 a - b} + \frac{- (3 a - b)}{- b + 2 a}$

Reorder terms.

$\frac{a}{2 a - b} + \frac{- (3 a - b)}{2 a - b}$

Combine the numerators over the common denominator.

$\frac{a - (3 a - b)}{2 a - b}$

Simplify the numerator.

Apply the distributive property.

$\frac{a - (3 a) - - b}{2 a - b}$

Multiply $3$ by $- 1$ .

$\frac{a - 3 a - - b}{2 a - b}$

Multiply $- - b$ .

Multiply $- 1$ by $- 1$ .

$\frac{a - 3 a + 1 b}{2 a - b}$

Multiply $b$ by $1$ .

$\frac{a - 3 a + b}{2 a - b}$

Subtract $3 a$ from $a$ .

$\frac{- 2 a + b}{2 a - b}$

Cancel the common factor of $- 2 a + b$ and $2 a - b$ .

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

$\frac{- (2 a) + b}{2 a - b}$

Factor $- 1$ out of $b$ .

$\frac{- (2 a) - 1 (- b)}{2 a - b}$

Factor $- 1$ out of $- (2 a) - 1 (- b)$ .

$\frac{- (2 a - b)}{2 a - b}$

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

$\frac{- 1 (2 a - b)}{2 a - b}$

Cancel the common factor.

$\frac{- 1 (2 a - b)}{2 a - b}$

Divide $- 1$ by $1$ .

$- 1$