Question 1023155
Call the original fraction
{{{x / (x+3)}}}
Then we add one to top and bottom and get
{{{(x-1) / (x+2)}}}
This fraction is 1/14 less than the original...thus we have to solve
{{{x / (x+3) - 1/14 = (x-1) / (x+2)}}}
Now multiply everything by the lowest common denominator...
{{{(14(x+2)(x+3))*(x/(x+3) - 1/14) = (14(x+2)(x+3))*((x-1) / (x+2))}}}
and we get
14x(x+2) - (x+2)(x+3) = 14(x+3)(x-1)
14x^2 + 28x - x^2 - 5x - 6 = 14x^2 + 28x - 42
The 14x^2 and 28x cancel out...
-x^2 - 5x - 6 = -42
x^2 + 5x + 6 = 42
x^2 + 5x - 36 = 0
(x + 9)(x - 4) = 0
x = -9 and x = 4
The original fraction must be
4/7.