Chapter 11.4, Problem 68SR

To determine

To calculate: To simplify the expression and state the excluded values of the variables

Answer to Problem 68SR

On simplifying, the expression is $\frac{p+3}{p-2}$ and the excluded value for the expression is $p=2$

Explanation of Solution

Given information: Expression is $\frac{p^2-9}{p^2-5p+6}$

Formula Used:

An excluded value is the value of variable for which the expression is undefined

Calculation:

Expression is given as

  $\frac{p^2-9}{p^2-5p+6}$

On simplifying the above expression

  $\begin{array}{l}\Rightarrow \frac{p^2-3^2}{p^2-3p-2p+6}\\ \Rightarrow \frac{\left(p-3\right)\left(p+3\right)}{p\left(p-3\right)-2\left(p-3\right)}\\ \Rightarrow \frac{\left(p-3\right)\left(p+3\right)}{\left(p-3\right)\left(p-2\right)}\\ \Rightarrow \frac{\left(p+3\right)}{\left(p-2\right)}\\ \Rightarrow \frac{p+3}{p-2}\end{array}$

The value of variable $p=2$ will make the expression undefined, thus excluded value for the expression is $p=2$

Conclusion:

Hence, on simplifying, the expression is $\frac{p+3}{p-2}$ and the excluded value for the expression is $p=2$