Simplify (11a-2b)/(4a)+(2a-3b)/(4a)-(a-b)/(4a)

$\frac{11 a - 2 b}{4 a} + \frac{2 a - 3 b}{4 a} - \frac{a - b}{4 a}$

Step 1

Combine the numerators over the common denominator.

$\frac{11 a - 2 b + 2 a - 3 b - (a - b)}{4 a}$

Step 2

Simplify each term.

Apply the distributive property.

$\frac{11 a - 2 b + 2 a - 3 b - a - - b}{4 a}$

Multiply $- - b$ .

Multiply $- 1$ by $- 1$ .

$\frac{11 a - 2 b + 2 a - 3 b - a + 1 b}{4 a}$

Multiply $b$ by $1$ .

$\frac{11 a - 2 b + 2 a - 3 b - a + b}{4 a}$

Step 3

Simplify terms.

Add $11 a$ and $2 a$ .

$\frac{13 a - 2 b - 3 b - a + b}{4 a}$

Subtract $a$ from $13 a$ .

$\frac{12 a - 2 b - 3 b + b}{4 a}$

Subtract $3 b$ from $- 2 b$ .

$\frac{12 a - 5 b + b}{4 a}$

Add $- 5 b$ and $b$ .

$\frac{12 a - 4 b}{4 a}$

Cancel the common factor of $12 a - 4 b$ and $4$ .

Factor $4$ out of $12 a$ .

$\frac{4 (3 a) - 4 b}{4 a}$

Factor $4$ out of $- 4 b$ .

$\frac{4 (3 a) + 4 (- b)}{4 a}$

Factor $4$ out of $4 (3 a) + 4 (- b)$ .

$\frac{4 (3 a - b)}{4 a}$

Cancel the common factors.

Factor $4$ out of $4 a$ .

$\frac{4 (3 a - b)}{4 (a)}$

Cancel the common factor.

$\frac{4 (3 a - b)}{4 a}$

Rewrite the expression.

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