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

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.

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