Question

The denominator of a fraction is four more than the numerator. If both numerator and denominator are increased by eight, the simplified result is 5/6. Find the original fraction.

Answer 1

The denominator of the fraction is four more than the numerator. The fraction:

`(x)/(x+4)`

If both numerator and denominator are increased by eight, the simplified result is 5/6:

`(x+8)/(x+4+8)=(5)/(6) \\ \\ (x+8)/(x+12)=(5)/(6) \ \ \ |* (x+12) \\ \\ x+8=(5)/(6)x+(5)/(6) * 12 \\ \\ x+8=(5)/(6)x+10 \\ \\ x-(5)/(6)x=10-8 \\ \\ (1)/(6)x=2 \ \ \ |* 6 \\ \\ x=12 \\ \\ (x)/(x+4)=(12)/(12+4)=\boxed{(12)/(16)}`

The original fraction is 12/16.