
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