Question

The area of a field can be expressed as A = 2x + 6 / x + 1 square yards. If the length is

L = x^2 - 9 / 2x + 10 what is the width? Show all work.

Answer 1

The width of the field is 4x + 20 / x² -2x -3 yards

Explanation:

The area of a rectangular field is given by the following formula:

area = length*width

In this case we want to find the width of this field, therefore if we isolate the width in the expression above we will have a suitable expression:

width*length = area

width = area / length

So applying the data from the problem, we have:

width = [(2x + 6)/(x + 1)] / [(x² - 9)/(2x + 10)]

width = [(2x + 6)/(x + 1)]*[(2x + 10)/(x² - 9)]

width = 2(x + 3)*(2x + 10) / (x+1)*(x - 3)*(x + 3)

width = 2*(2x + 10) / (x + 1)*(x - 3)

width = 4x + 20 / x² -2x -3