# the area of a rectangle is represented by fraction numerator x to the power of 4 minus y to the power of 4 over denominator 8 x y end fraction and its length is represented by fraction numerator x squared minus y squared over denominator 2 x y end fract

1. The Area of a rectangle is represented by and its length is represented by .

- What is the width of the rectangle?
- If you double the length of the rectangle but keep the same width, what is the new area of the rectangle?

2. Consider the following expression:

- Subtract the rational expressions
- Given the equation , solve the equation using your solution from part a.
- Solve the equation using LCD.
- Compare the methods used to solve the equation in parts c and d. Which method do you think is better and why?

3. The average cost of electricity used for an 18 cubic ft. refrigerator that is 10 years old is $128 per year. A new refrigerator the same size costs about $81 per year for electricity. (Source: https://www.efficiencyvermont.com)

- Suppose a new refrigerator costs $500. Determine the total cost of having either refrigerator for 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.
- Determine the total annual cost for a new refrigerator that lasts 12 years, assuming the only costs associated with the refrigerator are its purchase cost and electricity.
- Write a function that gives the annual cost of a new refrigerator as a function of the number of years you own the refrigerator.
- What are the asymptotes of the rational function in part d? What does the horizontal asymptote mean in the context of this problem?
- Sketch the graph of the rational function from part c.
- If you plan on owning your refrigerator for 12 years, would it be more cost effective to keep your old refrigerator or purchase a new one? Explain.