The numerator is one more than the denominator. If the numerator and denominator are both increased by two, the new fraction will be 1/4 less than the original fraction. What is the original fraction?

Answer 1

Hi Emily C.,

For the numerator one more than the denominator, (x+1)/x, (original fraction).

Both increased by 2, [(x+1)+2]/(x+2), (new fraction)

The new fraction = original fraction - 1/4

[(x+1)+2]/(x+2) = (x+1)/x -1/4, (solve for x)

I'll let you do the algebra. The answers for x are 2, and -4, which makes the original fraction 3/2, with either x value.

I hope this helps, Joe.

Answer 2

(x + 1 + 2) / (x + 2) = [(x + 1) / (x)] - [1 / 4]

(x + 3) / (x + 2) = [4(x + 1) - x] / 4x

(x + 3) / (x + 2) = (3x + 4) / 4x

4x (x + 3) = (x + 2) (3x + 4)

4x² + 3x = 3x² + 7x + 8

x² - 4x - 8 = 0

(x - 4)(x + 2) = 0

{-2, 4}