Question

A fraction becomes 1/2 if 5 is subtracted from its numerator and 3 is subtracted from its denominator. If the denominator of this fraction is 5 more than its numerator, find the fraction.

Answer 1

let fraction =x/y
x-5/y-3=1/2
2x-10=y-3
2x-y=7----(1)eq.
y=x+5
put this in (1)
2x-(x+5)=7
2x-x-5=7
x=7+5
x=12
y=x+5
y=12+5=17
fraction =12/17
it is correct

Answer 2

x/y is fraction
(x-5)/(y-3)=1/2
cross multiply
2x-10=y-3
2x-7=y
------------------
(x/2)/(y+7)=1/4
cross multiply
2x=y+7
y=2x-7
-----------------
any x will work, although the fraction is undefined for x=3.
try 1
y will be -5
(1-5)/-5-3)=-4/-8=1/2
(1/2)/2=(1/4)
-------------
Try x=-2, y=-11
-2-5/-11-3=-7/-14=1/2
(-2/2)/-11+7=-1/-4=1/4
The fraction is
x/2x-7
Try 3.5, which would make this fraction's denominator 0; y=0
-1.5/-3=1/2
1.75/7=1/4