Question

Subtract$\frac{3b}{b-2}-\frac{b-6}{b-8}$.

Short answer

The difference is$\frac{2(b^2-8b-6)}{(b-2)(b-8)}$.

Step-by-step solution

Given Information 

The Given expression is$\frac{3b}{b-2}-\frac{b-6}{b-8}$.

Find the LCD of denominators.  

Since there are no common denominators.

The LCD is$(b-2)(b-8)$.

Rewrite each fraction as an equivalent fraction with the LCD.   

$=\frac{3b(b-8)}{(b-2)(b-8)}-\frac{(b-6)(b-2)}{(b-2)(b-8)}$

Simplify numerator.

$=\frac{3b^2-24b}{(b-2)(b-8)}-\frac{b^2-2b-6b+12}{(b-2)(b-8)}$

Subtract and simplify the numerator.  

Take common denominator.

$=\frac{3b^2-24b-(b^2-8b+12)}{(b-2)(b-8)}$

$=\frac{3b^2-24b-b^2+8b-12}{(b-2)(b-8)}$

Simplify numerator.

$=\frac{2b^2-16b-12}{(b-2)(b-8)}$

$=\frac{2(b^2-8b-6)}{(b-2)(b-8)}$