Answer
3/4
Work Step by Step
We call x the numerator and y the denominator. Thus, we obtain:
$ \frac{x+5}{y-1} = \frac{8}{3} \\ 3x+15 = 8y-8 \\ 8y -3x = 23$
And
$ \frac{2x}{y+7} = \frac{6}{11} \\ 22x = 6y+42\\ x = .2727y + 1.90909$
We substitute equation two into equation one to obtain:
$8y -3(.2727y + 1.90909) = 23 \\ 8y - .81818y -5.2727 = 23 \\ y =4$
We plug in the given value into the second equation and solve for the other variable:
$ x = .2727(4) + 1.90909 = 3$
Thus, the fraction is 3/4.
