Chapter 6.1, Problem 2OE

To determine

To calculate: The simplified form of the expression $\frac{2n+8}{3n+12}$ and state restrictions on variable.

Answer to Problem 2OE

The simplified value of the expression $\frac{2n+8}{3n+12}$ is $\frac{2}{3}$ and restriction is $n\ne -4$.

Explanation of Solution

Given information:

The expression $\frac{2n+8}{3n+12}$.

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 $\frac{2n+8}{3n+12}$.

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 2 common from the numerator and 3 from the denominator then strike out common terms and simplify it as,

  $\begin{array}{c}\frac{2n+8}{3n+12}=\frac{2\left(n+4\right)}{3\left(n+4\right)}\\ =\frac{2}{3}\end{array}$

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

So, denominator will be zero when

  $\begin{array}{c}3n+12=0\\ 3n=-12\\ n=\frac{-12}{3}\\ n=-4\end{array}$.

For denominator not to be zero, $n\ne -4$.

Thus, the simplified value of the expression $\frac{2n+8}{3n+12}$ is $\frac{2}{3}$ and restriction is $n\ne -4$.