Chapter 6.6, Problem 14OE

To determine

Simplify: the given expression as fraction.

Answer to Problem 14OE

The simplified form of $4-\frac{1}{y+3}$ is $\frac{4y+11}{y+3}$.

Explanation of Solution

Given information:

The expression $4-\frac{1}{y+3}$.

Formula used:

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

  $4-\frac{1}{y+3}$

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

  $=\frac{4}{1}-\frac{1}{y+3}$

Least common denominator for $\frac{4}{1},\frac{1}{y+3}$ is $y+3$ . So,

  $\begin{array}{l}=\frac{4\left(y+3\right)-1}{y+3}\\ =\frac{4y+12-1}{y+3}\\ =\boxed{\frac{4y+11}{y+3}}\end{array}$

The simplified form of $4-\frac{1}{y+3}$ is $\frac{4y+11}{y+3}$.