Q. 24 - Intermediate Algebra

Question

Simplify the rational expression $\frac{4v-32}{64-v^2}$

Step-by-Step Solution

Answer

Simplified for the rational expression $\frac{4v-32}{64-v^2} is \frac{-4}{8-v} ,v\ne 8$

Step 1 . Given information

Rational expression here is $\frac{4v-32}{64-v^2} .$

We need to simplify the given rational expression.

Step 2 . Simplification of rational expression

To simplify the  factor the both numerator and denominator and find out the common factor ,so $\frac{4v-32}{64-v^2} =\frac{4(v-8)}{(8+v)(8-v)}$.We can see that common factors are opposite  to its .Hence $$\begin{gathered} \frac{4v-32}{64-v^2}=\frac{4(v-8)}{(8+v)(8-v)} \\ =\frac{-4(8+v)}{(8+v)(8-v)} \sin ce an expression opposites to its divides is -1 \\ =\frac{-4}{8-v } , v\ne 8 , here common factors ate divide out. \end{gathered}$$