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

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

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

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

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

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

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

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

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

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

Reorder terms.

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

Combine the numerators over the common denominator.

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

Rewrite $\frac{2 a + b - (a + 3 b)}{a - 2 b}$ in a factored form.

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Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Subtract $a$ from $2 a$ .

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

Subtract $3 b$ from $b$ .

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

Reduce the expression by cancelling the common factors.

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Reduce the expression $\frac{a - 2 b}{a - 2 b}$ by cancelling the common factors.

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Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{1}$

Rewrite the expression.

$1$

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

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