Chapter 6.1, Problem 1OE

To determine

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

Answer to Problem 1OE

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

Explanation of Solution

Given information:

The expression $\frac{3m+9}{m+3}$.

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 $\frac{3m+9}{m+3}$.

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 numerator and then strike out common terms and simplify it as,

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

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

So, denominator will be zero when $\begin{array}{c}m+3=0\\ m=-3\end{array}$.

For denominator not to be zero, $m\ne -3$.

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