SOLUTION: The numerator of a fraction is 1 less than the denominator.When both numerator and denominator are increased by 2, the fraction is increased by 1/12. find the orignal fraction.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The numerator of a fraction is 1 less than the denominator.When both numerator and denominator are increased by 2, the fraction is increased by 1/12. find the orignal fraction.      Log On


   

Question 165928: The numerator of a fraction is 1 less than the denominator.When both numerator and denominator are increased by 2, the fraction is increased by 1/12. find the orignal fraction.
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
fraction is (x-1)/x
fraction with numerator and denominator increased by 2 is (x+1)/(x+2)
the fraction is increased by 1/12
then (x-1)/x + 1/12 = (x+1)/(x+2)

(12(x-1)+x)/12x = (x+1)/(x+2)
(13x-12)/12x = (x+1)/(x+2)
(13x-12)(x+2)=12x(x+1)
13x^2+14x-24=12x^2+12x
x^2+2x-24=0
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-24%29+%29%29%2F%282%29+
then
x+=+%28-2+%2B-+10+%29%2F%282%29+
x=-6 or x=4
assuming numerator and denominator possitive
then x=4 and fraction is 3/4