Andy C. answered • 08/27/17

Math/Physics Tutor

Hello Talal. Hope all is well.

We know nothing about the numerator, so

THAT is where we assign the variable.

Let N be the numerator of the fraction.

Then the denominator is 3N-1 <--- it is 1 less than 3 times the numerator.

So the fraction looks like this:

N

-------------

3N - 1

Now what happens next is if both the numerator and the denominator

are increased by 3, the fraction becomes 1/2

so the fraction becomes:

N+3 1

------------ = -------

3N - 1+3 2

The denominator can be simplified:

N+3 1

-------- = ----------

3N + 2 2

Cross multiplication :

2(N+3) = 1*(3N+2)

2N + 6 = 3N + 2 <---- distributive property

0 = 3N + 2 - 2N - 6 <---- moves everything to the right side

0 = N - 4 <--- combines like terms

N = 4 <--- solves for N

So the numerator is 4

Then the denominator is 3*4 - 1 = 11

So the original fraction is 4/11

When 3 is added to both the numerator and denominator,

the fraction becomes 7/14 which does reduce to 1/2.

The original fraction is 4/11