EDGE Math 8

Problems Involving Rational Expressions

Example 1

A rectangular picture frame has a length of $(\frac{6 p}{p^{2} + 5 p + 6})$ cm and a width of $(\frac{6 p + 6}{p + 3})$ cm. Solve for the following and express each answer in simplest form:

a. area of the frame

b. perimeter of the frame

Solution

a. Let A be the area of the rectangular picture frame. The area of a rectangle is equal to the product of its length and its width.

A = (\frac{6 p}{p^{2} + 5 p + 6}) (\frac{6 p + 6}{p + 3})

= \frac{6 p}{(p + 3) (p + 2)} \cdot \frac{3 (p + 2)}{p + 3}

= \frac{(6 p) (3) (p + 2)}{(p + 3) (p + 2) (p + 3)}

= \frac{18 p}{{(p + 3)}^{2}}

Thus, the area of the frame is $\frac{18 p}{{(p + 3)}^{2}} {cm}^{2} .$

(Continuation on the next slide)