Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $b$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Simplify the expression.

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Step 1.4.1

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

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

Step 1.4.2

Reorder terms.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $3$ by $- 1$ .

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

Step 2.3

Multiply $- - b$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

Multiply $b$ by $1$ .

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

Step 2.4

Subtract $3 a$ from $a$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Factor $- 1$ out of $b$ .

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Divide $- 1$ by $1$ .

$- 1$