Chapter A.3, Problem 37E

Solution

Write the expression in reduced form.

  $\frac{z^2-3x}{(3+z)(3-z)}$ .

Given:

The given expression is $\frac{z^2-3x}{9-z^2}$ .

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 $\frac{z^2-3x}{9-z^2}$ .

  $\begin{array}{c}\frac{z^2-3x}{9-z^2}=\frac{z^2-3x}{3^2-z^2}\\ =\frac{z^2-3x}{(3+z)(3-z)}\end{array}$

Thus the reduced form of $\frac{z^2-3x}{9-z^2}$ is $\frac{z^2-3x}{(3+z)(3-z)}$ .