SOLUTION: The denominator of the fraction is 2 more than the numerator. If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1/2. Find the original f

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Question 389491: The denominator of the fraction is 2 more than the numerator. If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1/2. Find the original fraction. (Need a complete solution for this. Thanks)
Found 2 solutions by MathLover1, ptaylor:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The denominator of the fraction is 2 more than the numerator. If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1/2. Find the original fraction. (Need a complete solution for this. Thanks)

let the numerator be x and denominator y

given: the denominator of the fraction is 2 more than the numerator ; so, y=x%2B2
the fraction is
x%2F%28x%2B2%29
If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1%2F2, so we will have
%28x-1%29%2F%28x%2B2-1%29=1%2F2
%28x-1%29%2F%28x%2B1%29=1%2F2...cross multiply
2%28x-1%29=1%28x%2B1%29
2x-2=1x%2B1..........solve for x
2x-+x+=+2%2B1
x+=+3..........the numerator
y=x%2B2
y=3%2B2
y=5..........the denominator
so, fraction is 3%2F5
check:
If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1%2F2, so we will have
%283-1%29%2F%285-1%29=2%2F4=1%2F2

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=numerator
Then x+2=denominator
So our equation to solve is:
(x-1)/(x+2-1)=1/2 simplifying we have
(x-1)/(x+1)=1/2 now multiply each side by 2(x+1)
2(x-1)=x+1
2x-2=x+1 subtract x from and add 2 to each side:
2x-x-2+2=x-x+1+2 collect like terms
x=3
CK
(3-1)/(3+1)=1/2
2/4=1/2
1/2=1/2
Hope this helps---ptaylor