Rational Expression Word Problem

Question

You are carpeting a room in a house for your job.  You have a boss that likes to play jokes, so instead of just giving you the dimensions of the room, he tells you the dimensions in rational expressions.  The length of the room is x²-3x+2/x+5  and the width of the room is x²+7x+10/x-2  .

What is the area of the room in terms of x?  How much carpet do you need if x = 15?

Answer 1

(x^2 -3x +2)/(x+5) = (x-1)(x-2)/(x+5)

(x^2 +7x +10)/(x-2) = (x+5)(x+2)/(x-2)

area = length times width = (x-1)(x-2)/(x+5) times (x+5)(x+2)/(x-2) = (x-1)(x+2)

area = x^2 +x -2

if x = 15 then the area =(15-1)(15+2) = 14(17) = 238

or 15^2 + 15 -2 = 225 +13 = 238