Chantel is carpeting a room that has an area of x^2-100 square feet. If the width of the room is x-10 feet, what is the length of the room.

A=LW and we are told that:

A=x^2-100 and W=x-10 so:

x^2-100=L (x-10)

L = (x^2-100) / (x-10) factoring the numerator ...

L = ((x+10) (x-10)) / (x-10) the (x-10) terms cancel out leaving ...

L=x+10