Chapter 11.4, Problem 67SR

To determine

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

Answer to Problem 67SR

On simplifying, the expression is $\left(y+8\right)$ and there is no excluded value of the expression

Explanation of Solution

Given information: Expression is $\frac{y^2+10y+16}{y+2}$

Formula Used:

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

Calculation:

Expression is given as

  $\frac{y^2+10y+16}{y+2}$

On simplifying the above expression

  $\begin{array}{l}\Rightarrow \frac{y^2+2y+8y+16}{y+2}\\ \Rightarrow \frac{y\left(y+2\right)+8\left(y+2\right)}{y+2}\\ \Rightarrow \frac{\left(y+2\right)\left(y+8\right)}{y+2}\\ \Rightarrow \left(y+8\right)\end{array}$

Since there is no variable in the denominator, thus there is no excluded value of the expression

Conclusion:

Hence, on simplifying, the expression is $\left(y+8\right)$ and there is no excluded value of the expression