Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Reorder terms.

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

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

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Step 7.1

Apply the distributive property.

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

Step 7.2

Multiply $3$ by $- 1$ .

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

Step 7.3

Subtract $a$ from $2 a$ .

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

Step 7.4

Subtract $3 b$ from $b$ .

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

Step 7.5

Reduce the expression by cancelling the common factors.

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Step 7.5.1

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

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Step 7.5.1.1

Cancel the common factor.

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

Step 7.5.1.2

Rewrite the expression.

$\frac{1}{1}$

Step 7.5.2

Rewrite the expression.

$1$