Simplify (6a+5b)/(8a-2b)-(a+6b)/(8a-2b)+(3a-b)/(8a-2b)

$\frac{6 a + 5 b}{8 a - 2 b} - \frac{a + 6 b}{8 a - 2 b} + \frac{3 a - b}{8 a - 2 b}$

Combine the numerators over the common denominator.

$\frac{6 a + 5 b - (a + 6 b) + 3 a - b}{8 a - 2 b}$

Simplify each term.

Apply the distributive property.

$\frac{6 a + 5 b - a - (6 b) + 3 a - b}{8 a - 2 b}$

Multiply $6$ by $- 1$ .

$\frac{6 a + 5 b - a - 6 b + 3 a - b}{8 a - 2 b}$

Simplify terms.

Subtract $a$ from $6 a$ .

$\frac{5 a + 5 b - 6 b + 3 a - b}{8 a - 2 b}$

Add $5 a$ and $3 a$ .

$\frac{8 a + 5 b - 6 b - b}{8 a - 2 b}$

Subtract $6 b$ from $5 b$ .

$\frac{8 a - b - b}{8 a - 2 b}$

Subtract $b$ from $- b$ .

$\frac{8 a - 2 b}{8 a - 2 b}$

Cancel the common factor of $8 a - 2 b$ .

Cancel the common factor.

$\frac{8 a - 2 b}{8 a - 2 b}$

Rewrite the expression.

$1$