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 388168: 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 Answer by aggie_tutor(13) (Show Source):
You can put this solution on YOUR website! Let numerator = x
Problem statment: demoninator = (x+2)
So the fraction looks like:
x/(x+2)
Second part of problem statement:
Numerator (x-1)
Denominator (x+2)-1
So the new fraction (forget about the old one!) looks like:
For subtraction simplifies to:
Set the equation. Problem statement says this fraction thing is equal to 1/2.
The 1/2 fraction doesn't look too nice so let's just make it 1. We can do that by multiplying both sides of the equation by 2, i.e. 2/1.
The right side just becomes 1 (the 2s cancel out.)
The left side is tricky. You must multiply the numerator by 2 only. becomes
The denominator is multiplied by 1, so it does not change at all.
The new left side and right side of the equation is now:
Much nicer to look at. And when we have a fraction = 1, we can always multiply both sides by the denominator (x+1). This cancels the denominator on the left, and moves the (x+1) to the right side. This gets rid of the fraction, which is what we wanted.
Combine like terms. We can put x terms on the left, and the constant (non-x) terms on the right. First subtract x from both sides.
Now add 2 to both sides.
Check your answer by putting x into the original equation.
