Algebra Examples

$\frac{2 a + b}{{(a - b)}^{2}} + \frac{2 b - 5 a}{{(a - b)}^{2}}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{2 a + b + 2 b - 5 a}{{(a - b)}^{2}}$

Step 1.2

Subtract $5 a$ from $2 a$ .

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

Step 1.3

Add $b$ and $2 b$ .

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

Step 1.4

Factor $3$ out of $- 3 a + 3 b$ .

Tap for more steps...

Step 1.4.1

Factor $3$ out of $- 3 a$ .

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

Step 1.4.2

Factor $3$ out of $3 b$ .

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

Step 1.4.3

Factor $3$ out of $3 (- a) + 3 (b)$ .

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

Step 1.5

Cancel the common factor of $- a + b$ and ${(a - b)}^{2}$ .

Tap for more steps...

Step 1.5.1

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

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

Step 1.5.2

Factor $- 1$ out of $b$ .

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

Step 1.5.3

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

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

Step 1.5.4

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

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

Step 1.5.5

Factor $a - b$ out of $3 (- 1 (a - b))$ .

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

Step 1.5.6

Cancel the common factors.

Tap for more steps...

Step 1.5.6.1

Factor $a - b$ out of ${(a - b)}^{2}$ .

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

Step 1.5.6.2

Cancel the common factor.

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

Step 1.5.6.3

Rewrite the expression.

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

Step 2

Multiply $3$ by $- 1$ .

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

Step 3

Move the negative in front of the fraction.

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