Chapter A.3, Problem 39E

Solution

Write the expression in reduced form.

  $\frac{(y+5)}{(y+3)}$ .

Given:

The given expression is $\frac{y^2-y-30}{y^2-3y-18}$ .

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 $\frac{y^2-y-30}{y^2-3y-18}$ .

  $\begin{array}{c}\frac{y^2-y-30}{y^2-3y-18}\\ solve{y}^2-y-30=y^2-(6-5)y-30\\ =y^2-6y+5y-30\\ =y(y-6)+5(y-6)\\ =(y+5)(y-6)\\ solve{y}^2-3y-18=y^2-(6-3)y-18\\ =y^2-6y+3y-18\\ =y(y-6)+3(y-6)\\ =(y+3)(y-6)\\ putthevalueabove\\ \frac{y^2-y-30}{y^2-3y-18}=\frac{(y+5)(y-6)}{(y+3)(y-6)}\\ =\frac{(y+5)}{(y+3)}\end{array}$

Thus the reduced form of $\frac{y^2-y-30}{y^2-3y-18}$ is $\frac{(y+5)}{(y+3)}$ .