Q. 18 - Intermediate Algebra

Question

Simplify the rational expression $\frac{-5c^2-10c}{-10c^2+30c+100}.$

Step-by-Step Solution

Answer

Simplified form of $\frac{-5c^2-10c}{-10c^2+30c+100} is \frac{c}{5(c-5) } ;c\ne 5$

Step 1 . Given information

Given  rational expression is $\frac{-5c^2-10c}{-10c^2+30c+100}$

We have to simplify the given rational expression.

Step 2 . Simplification of rational expression

To simplify factor numerator and denominator and divide out the common factor , hence simplified form is  

$$\begin{gathered} \frac{-5c^2-10c}{-10c^2+30c+100}=\frac{-5c(c+2)}{-10(c^2-3c-10)} \\ =\frac{-5c(c+2)}{-10(c-5)(c+2)} , divide out common factors \\ =\frac{c}{c-5} ;c\ne 5 \end{gathered}$$