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.

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

Step-by-step 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