Q . 20 - Intermediate Algebra

Question

Simplify the rational expression $\frac{5r^2+30rs-35s^2}{r^2-49s^2}$$\frac{5r^2+30rs-35s^2}{r^2-49s^2}$

Step-by-Step Solution

Answer

Simplified form of

 $\frac{5r^2+30rs-35s^2}{r^2-49s^2} is \frac{5(r-1s)}{(r-7s)} ; r\ne 7s.$ 

Step 1 . Given information

Given rational expression is $\frac{5r^2+30rs-35s^2}{r^2-49s^2} .$

We need  to simplify the given rational expression.

Step 2 . Simplify the rational expression

To simplify  we have to factor  both numerator and denominator separately and divide out the common factor .Then the simplified form is 

 $$\begin{gathered} \frac{5r^2+30rs-35s^2}{r^2-49s^2}=\frac{5(r^2+6rs-7s)}{(r+7s)(r-7s)} \\ =\frac{5(r+7s)(r-1s)}{(r+7s)(r-7s)} \\ =\frac{5(r-1s)}{(r-7s)} ;r\ne 7s \end{gathered}$$