Chapter 9.7, Problem 9MRE

To determine

To simplify: the expression $\frac{4+c}{2+c}-\frac{1}{2}$ .

Answer to Problem 9MRE

The value is $\frac{3}{2}$ .

Explanation of Solution

Given information:

  $\frac{4+c}{2+c}-\frac{1}{2}$

Formula used:

Order of operations:

Step 1. Evaluate expressions inside grouping symbols.

Step 2. Evaluate all powers.

Step 3. Multiply and / or divide from left to right.

Step 4. Add and/or subtract from left to right.

Calculation:

Consider ,

  $\frac{4+c}{2+c}-\frac{1}{2}$

Taking L.C.M. we get,

  $\begin{array}{l}=\left(\frac{4+c}{2+c}\times \frac{2}{2}\right)-\left(\frac{1}{2}\times \frac{2+c}{2+c}\right)\\ =\left(\frac{2(4+c)}{2(2+c)}\right)-\left(\frac{2+c}{2(2+c)}\right)\\ =\frac{2(4+c)-2+c}{2(2+c)}\\ =\frac{8+2c-2+c}{2(2+c)}\\ =\frac{6+3c}{2(2+c)}\\ =\frac{3(2+c)}{2(2+c)}\\ =\frac{3}{2}\end{array}$

Hence, the value is $\frac{3}{2}$ .