Chapter 6.6, Problem 13OE

To determine

Simplify: the given expression as fraction.

Answer to Problem 13OE

The simplified form of $2+\frac{3}{x+1}$ is $\frac{2x+5}{x+1}$.

Explanation of Solution

Given information:

The expression $2+\frac{3}{x+1}$.

Formula used:

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

  $2+\frac{3}{x+1}$

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

  $=\frac{2}{1}+\frac{3}{x+1}$

Least common denominator for $\frac{2}{1},\frac{3}{x+1}$ is $x+1$ . So,

  $\begin{array}{l}=\frac{2\left(x+1\right)+3}{x+1}\\ =\frac{2x+2+3}{x+1}\\ =\boxed{\frac{2x+5}{x+1}}\end{array}$

The simplified form of $2+\frac{3}{x+1}$ is $\frac{2x+5}{x+1}$.