Chapter 8.1, Problem 14PPS

To determine

Simplify the given expression.

Answer to Problem 14PPS

The required simplified expression is $\frac{y\left(y+1\right)}{2\left(y-4\right)}$ .

Explanation of Solution

Given information: Given the expression is $\frac{y^2\left(y^2+3y+2\right)}{2y\left(y-4\right)\left(y+2\right)}$ .

Calculation:

Given the expression:

  $\begin{array}{l}\frac{y^2\left(y^2+3y+2\right)}{2y\left(y-4\right)\left(y+2\right)}\\ =\frac{y^2\left(y^2+y+2y+2\right)}{2y\left(y-4\right)\left(y+2\right)}\\ =\frac{y^2\left[y\left(y+1\right)+2\left(y+1\right)\right]}{2y\left(y-4\right)\left(y+2\right)}\\ =\frac{y^2\left(y+2\right)\left(y+1\right)}{2y\left(y-4\right)\left(y+2\right)}\\ =\frac{y^2\left(y+1\right)}{2y\left(y-4\right)}\text{ cancel out like terms}\\ =\frac{y\left(y+1\right)}{2\left(y-4\right)}\end{array}$

Thus, the required simplified expression is $\frac{y\left(y+1\right)}{2\left(y-4\right)}$