Question

Simplify the rational expression$\frac{3m^2+30mn+75n^2}{4m^2-100n^2}$

Short answer

Simplified form of rational expression$\frac{3m^2+30mn+75n^2}{4m^2-100n^2}is\frac{3(m+5n)}{4(m-5n)};5n\ne 5.$

Step-by-step solution

. Given information

Given rational expression is $\frac{3m^2+30mn+75n^2}{4m^2-100n^2}.$

Simplify the given rational expression

.  Simplification of rational expression

First, we have to find out the factor of both numerator and denominator, divide out the common factor and then simplify. Hence simplified form is

$$\begin{gathered} \frac{3m^2+30mn+75n^2}{4m^2-100n^2}=\frac{3(m^2+10mn+25n^2)}{4(m^2-25n^2)} \\ =\frac{3(m+5n)(m+5n)}{4(m+5n)(m-5n)},(m+5n)iscommonfactorsodivideout \\ =\frac{3(m+5n)}{4(m-5n)};m\ne 5n \end{gathered}$$