SOLUTION: What is the denominator of a fraction is 1 greater than its numerator. If both the numerator and demonminator are decreased by 3, the resulting fraction is equal to 4 timesthe ori

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Question 191372: What is the denominator of a fraction is 1 greater than its numerator. If both the numerator and demonminator are decreased by 3, the resulting fraction is equal to 4 timesthe original fraction. Find the original fraction.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numerator of the original fraction is x, the the original fraction can be expressed as:
x%2F%28x%2B1%29
The resulting fraction is
%28x-3%29%2F%28x%2B1-3%29=%28x-3%29%2F%28x-2%29
As the resulting fraction is equal to 4 timesthe original fraction, we have
%28x-3%29%2F%28x-2%29=4x%2F%28x%2B1%29
Solving for x, we have
4x%28x-2%29=%28x-3%29%28x%2B1%29 cross-multiplication
4x%5E2-8x=x%5E2-2x-3 expanding
3x%5E2-6x%2B3=0
x%5E2-2x%2B1=0 dividing both sides by 3 to simplify the equation
%28x-1%29%5E2=0
So x = 1
Therefore the original fraction is x%2F%28x%2B1%29=1%2F%281%2B1%29=1%2F2