Chapter 6, Problem 2CT

To determine

To evaluate:

The value of the given number

Answer to Problem 2CT

The value of given operation is $-\frac{\left(8+4\right)}{\left(n+4\right)}$

Explanation of Solution

Given:

The order of operation

  $\frac{64-n^2}{n^2-4n-32}$

Concept used:

Product means the answer to a multiplication problem

Sum means the total amount resulting from the addition of two or more numbers amounts or items

Quotientmeansa result obtained by dividing one quantity by another

Calculation:

The order of operation

  $\begin{array}{l}=\frac{64-n^2}{n^2-4n-32}\\ =\frac{8^2-n^2}{n^2-4n-32}\\ \text{factor}\text{of}\text{denominator}\\ n^2-4n-32\\ n^2-8n+4n-32\\ n\left(n-8\right)+4\left(n-8\right)\\ \left(n-8\right)\left(n+4\right)\\ =\frac{\left(8-n\right)\left(8+4\right)}{\left(n-8\right)\left(n+4\right)}\\ =-\frac{\left(8+4\right)}{\left(n+4\right)}\end{array}$

Therefore,

The value of given operation is $-\frac{\left(8+4\right)}{\left(n+4\right)}$