The original fraction is
.
Let the numerator be represented by x, and the denominator by y. So that;
=
............... 1
=
............ 2
From equation 1, we have;
2y - 6 = 3x +12
2y - 3x = 6 + 12
3x - 2y = -18.......................... 3
From equation 2, we have;
2x + 10 = y + 5
2x - y = -10 + 5
2x - y = -5 ....................... 4
Multiply equation 3 by 2, and equation 4 by 3 to have;
6x - 4y = -36 ........... 5
6x - 3y = - 15 ............. 6
subtract equation 6 from 5,
6x - 6x -4y + 3y = -36 + 15
-y = -21
y = 21
Substitute the value of y in equation 4,
2x - y = -5
2x - 21 = -5
2x = -5 + 21
2x = 16
x = 8
Thus, the original fraction is
.