Chapter 6.1, Problem 5WE

To determine

To calculate: The simplified form of the expression $\frac{3n+1}{9n+3}$ and state restrictions on variable.

Answer to Problem 5WE

The simplified value of the expression $\frac{3n+1}{9n+3}$ is $\frac{1}{3}$ and restriction is $n\ne -\frac{1}{3}$.

Explanation of Solution

Given information:

The expression $\frac{3n+1}{9n+3}$.

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 $\frac{3n+1}{9n+3}$.

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

  $\begin{array}{c}\frac{3n+1}{9n+3}=\frac{3n+1}{3\left(3n+1\right)}\\ =\frac{1}{3}\end{array}$

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

So, denominator will be zero when,

  $\begin{array}{c}9n+3=0\\ 9n=-3\\ n=\frac{-3}{9}\\ n=-\frac{1}{3}\end{array}$

For denominator not to be zero, $n\ne -\frac{1}{3}$.

Thus, the simplified value of the expression $\frac{3n+1}{9n+3}$ is $\frac{1}{3}$ and restriction is $n\ne -\frac{1}{3}$.