The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. what is the distance added to each side?

24*16 = 384

384*2 = 768

24+d * 16+d =768

384 + 40d+d^2 = 768

d^2 + 40d-384 =0

(d+48) (d-8) = 0

 d=-48, d=8 can't use a negative number so d = 8

check:

24+8=32, 16+8=24, 32x 24 = 768

 so 8 feet is added to each side

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.