Chapter 6.1, Problem 4OE

To determine

To calculate: The simplified form of the expression $\frac{b^2-9}{b+3}$ and state restrictions on variable.

Answer to Problem 4OE

The simplified value of the expression $\frac{b^2-9}{b+3}$ is $b-3$ and restriction is $b\ne -3$.

Explanation of Solution

Given information:

The expression $\frac{b^2-9}{b+3}$.

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 $\frac{b^2-9}{b+3}$.

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, factorize the numerator by using the formula of difference of squares $X^2-Y^2=\left(X+Y\right)\left(X-Y\right)$ and then strike out common terms and simplify it as,

  $\begin{array}{c}\frac{b^2-9}{b+3}=\frac{\left(b-3\right)\left(b+3\right)}{\left(b+3\right)}\\ =b-3\end{array}$

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

So, denominator will be zero when

  $\begin{array}{c}b+3=0\\ b=-3\end{array}$.

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

Thus, the simplified value of the expression $\frac{b^2-9}{b+3}$ is $b-3$ and restriction is $b\ne -3$.