Chapter 11: Q. 19 (page 1069)

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

Short Answer

Expert verified

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

Step by step solution

. Given information

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

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

$\frac{3 m^{2} + 30 m n + 75 n^{2}}{4 m^{2} - 100 n^{2}} = \frac{3 (m^{2} + 10 m n + 25 n^{2})}{4 (m^{2} - 25 n^{2})} = \frac{3 (m + 5 n) (m + 5 n)}{4 (m + 5 n) (m - 5 n)}, (m + 5 n) i s c o m m o n f a c t o r s o d i v i d e o u t = \frac{3 (m + 5 n)}{4 (m - 5 n)}; m \neq 5 n$

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

Short Answer

Step by step solution

. Given information

. Simplification of rational expression

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Simplify the rational expression3m2+30mn+75n24m2-100n2

Short Answer

Step by step solution

. Given information

. Simplification of rational expression

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Most popular questions from this chapter

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