Chapter 6.6, Problem 16WE

To determine

Simplify: the given expression as fraction.

Answer to Problem 16WE

The simplified form of $4y+\frac{y}{y-5}$ is $\frac{y\left(4y-19\right)}{y-5}$.

Explanation of Solution

Given information:

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

Formula used:

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

  $4y+\frac{y}{y-5}$

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

  $=\frac{4y}{1}+\frac{y}{y-5}$

Least common denominator for $\frac{4y}{1},\frac{y}{y-5}$ is $y-5$ . So,

  $\begin{array}{l}=\frac{4y\left(y-5\right)+y}{y-5}\\ =\frac{4y^2-20y+y}{y-5}\\ =\frac{4y^2-19y}{y-5}\\ =\boxed{\frac{y\left(4y-19\right)}{y-5}}\end{array}$

The simplified form of $4y+\frac{y}{y-5}$ is $\frac{y\left(4y-19\right)}{y-5}$.