Chapter 6.1, Problem 17WE

To determine

To calculate: The simplified form of the expression $\frac{4n^2+144}{6n+36}$ and state restrictions on variable.

Answer to Problem 17WE

The simplified value of the expression $\frac{4n^2+144}{6n+36}$ is $\frac{2\left(n^2+36\right)}{3\left(n+6\right)}$ and restriction is $n\ne -6$.

Explanation of Solution

Given information:

The expression $\frac{4n^2+144}{6n+36}$.

Formula used:

The simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ . Simplification is done by factorizing numerator and denominator.

Calculation:

Consider the expression $\frac{4n^2+144}{6n+36}$.

Recall that the simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ . Simplification is done by factorizing numerator and denominator.

So, take out $4$ common from numerator and $6$ from denominator and then strike out common terms from the expression and simplify it as,

  $\begin{array}{c}\frac{4n^2+144}{6n+36}=\frac{4\left(n^2+36\right)}{6\left(n+6\right)}\\ =\frac{2\left(n^2+36\right)}{3\left(n+6\right)}\end{array}$

To restrict the variable, exclude the value that makes the denominator zero.

So, denominator will be zero when,

  $\begin{array}{c}6n+36=0\\ 6n=-36\\ n=-6\end{array}$

For denominator not to be zero, $n\ne -6$.

Thus, the simplified value of the expression $\frac{4n^2+144}{6n+36}$ is $\frac{2\left(n^2+36\right)}{3\left(n+6\right)}$ and restriction is $n\ne -6$.