SOLUTION: the numerator of a certain fraction is 2 more than the denomenator. if 1/3 is added to the fracgion, the result is 2. find the fraction

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: the numerator of a certain fraction is 2 more than the denomenator. if 1/3 is added to the fracgion, the result is 2. find the fraction      Log On


   

Question 117495: the numerator of a certain fraction is 2 more than the denomenator. if 1/3 is added to the fracgion, the result is 2. find the fraction
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the denominator
:
"the numerator of a certain fraction is 2 more than the denomenator.
%28%28x%2B2%29%29%2Fx
:
"if 1/3 is added to the fraction, the result is 2"
%28%28x%2B2%29%29%2Fx + 1%2F3 = 2
:
find the fraction
Multiply equation by 3x to eliminate the denominators
3x*%28%28x%2B2%29%29%2Fx + 3x*1%2F3 = 3x(2)
:
Cancel out the denominators and you have:
3(x+2) + 1x = 6x
:
3x + 6 + x = 6x
:
4x + 6 = 6x
:
6 = 6x - 4x
:
6 = 2x
:
x = 6%2F2
:
x = 3
:
:
Check our solution in original equation
%28%283%2B2%29%29%2F3 + 1%2F3 = 2
:
%285%29%2F3 + 1%2F3 = 2; confirms our solution
:
Did I make this understandable, any questions?