Q . 26 - Intermediate Algebra

Question

Simplify the rational expression $\frac{v^3+125}{v^2-25}$

Step-by-Step Solution

Answer

Simplified form of the rational expression  $\frac{v^3+125}{v^2-25} is \frac{v^2-5v+25)}{v-5} ,v\ne 5$

Step 1 . Given information

Here given rational expression is $\frac{v^3+125}{v^2-25}.$We need to simplify the given rational expression.

Step 2 . Simplification of rational expression

To simplify the rational expression $\frac{v^3+125}{v^2-25}$first we need to factor the numerator and denominator  and divide out common factor. Thus given  expression  $$\begin{gathered} \frac{v^3+125}{v^2-25}=\frac{(v+5)(v^2-5v+25)}{(v+5)(v-5)} , \sin ce v^3+125 is inthe form of a^3+b^3=(a+b)(a^2-ab+b^2). \\ =\frac{(v^2-5v+25)}{(v-5)} ,v\ne 5 ,here (v+5) is commonfactor so divide out \end{gathered}$$