Chapter 6.6, Problem 9WE

To determine

Simplify: the given expression as fraction.

Answer to Problem 9WE

The simplified form of $5-\frac{4}{x+2}$ is $\frac{5x+6}{x+2}$.

Explanation of Solution

Given information:

The expression $5-\frac{4}{x+2}$.

Formula used:

Least common denominator: It is the smallest multiple of denominator of set of fractions.

  $5-\frac{4}{x+2}$

Recall that Least common denominator is the smallest multiple of denominator of set of fractions.

  $\frac{5}{1}-\frac{4}{x+2}$

Least common denominator for $\frac{5}{1},\frac{4}{x+2}$ is $x+2$ . So,

  $\begin{array}{l}=\frac{5\left(x+2\right)-4}{x+2}\\ =\frac{5x+10-4}{x+2}\\ =\boxed{\frac{5x+6}{x+2}}\end{array}$

The simplified form of $5-\frac{4}{x+2}$ is $\frac{5x+6}{x+2}$.