Q. 17 - Intermediate Algebra

Question

Simplify the rational expression$\frac{8b^2-32}{2b^2-6b-80}$

Step-by-Step Solution

Answer

Simplified form of rational expression $\frac{8b^2-32b}{2b^2-6b-80} is \frac{4b(b-4)}{(b+5)(b-8)} where b\ne -5,8$ 

Step 1 . Given information

Given rational expression is $\frac{8b^2-32b}{2b^2-6b-80}.$

Simplify the given rational expression.

Step 2 . Simplification of rational expression

For the  simplification factor both numerator and denominator separately  , divide out the common factor and then simplify.

Hence simplified for of the given expression is

 $$\begin{gathered} \frac{8b^2-32b}{2b^2-6b-80}=\frac{8b(b-4)}{2(b^2-3b-40)} \\ =\frac{8b(b-4)}{2(b+5)(b-8)} \\ =\frac{4b(b-4)}{(b+5)(b-8)} where b\ne -5,8,4 \end{gathered}$$