Chapter 7, Problem 1PCT

Evaluate $\frac{a^3-b^3}{a+b}$ when a = 2 and b = −3.

To determine

To evaluate: The expression $\frac{a^3-b^3}{a+b}$ for the values $a=2$ and $b=-3$.

Answer to Problem 1PCT

The value of the expression $\frac{a^3-b^3}{a+b}$ for the values $a=2$ and $b=-3$ is $-35$.

Explanation of Solution

Definition used:

Rational expression:

“A rational expression is the quotient of two polynomials. That is, a rational expression is written in the form $\frac{p}{q}$, where p and q are polynomials and $q\ne 0$”.

Calculation:

Consider the expression $\frac{a^3-b^3}{a+b}$.

Substitute $a=2$ and $b=-3$ in $\frac{a^3-b^3}{a+b}$ and simplify as follows.

$\begin{array}{c}\frac{a^3-b^3}{a+b}=\frac{{\left(2\right)}^3-{\left(-3\right)}^3}{2+\left(-3\right)}\\ =\frac{8-\left(-27\right)}{2-3}\\ =\frac{8+27}{-1}\\ =-35\end{array}$

Therefore, the value of the expression $\frac{a^3-b^3}{a+b}$ for the values $a=2$ and $b=-3$ is $-35$.