Chapter A.3, Problem 40E

Solution

Write the expression in reduced form.

  $\frac{y(y-3)}{(y-7)}$ .

Given:

The given expression is $\frac{y^3+4y^2-21y}{y^2-49}$ .

Concept Used:

• Factor the numerator and the denominator.
• List restricted values.
• Cancel common factors.
• Reduce to lowest terms and note any restricted values not implied by the expression.

Calculation:

The given expression is $\frac{y^3+4y^2-21y}{y^2-49}$ .

  $\begin{array}{c}\frac{y^3+4y^2-21y}{y^2-49}=\frac{y(y^2+4y-21)}{y^2-7^2}\\ =\frac{y(y^2+4y-21)}{(y+7)(y-7)}\\ solve{y}^2+4y-21=y^2+(7-3)y-21\\ =y^2+7y-3y-21\\ =y(y+7)-3(y+7)\\ =(y-3)(y+7)\\ putthevalueabove\\ \frac{y(y^2+4y-21)}{(y+7)(y-7)}=\frac{y(y-3)(y+7)}{(y+7)(y-7)}\\ =\frac{y(y-3)}{(y-7)}\end{array}$

Thus the reduced form of $\frac{y^3+4y^2-21y}{y^2-49}$ is $\frac{y(y-3)}{(y-7)}$ .