When 5 is added to both the numerator and denominator of a fraction the result becomes 1/2.When 1 is subtracted from both the numerator and denominator the fraction becomes 1/5.Find the fraction. plzz do whole method, i cant understand it.

Answer 1

original fraction: x/y

case1 (x+5)/(y+5) = 1/2
2x + 10 = y+5
2x - y = -5 **

case2 (x-1)/(y-1) = 1/5
5x - 5 = y - 1
5x - y = 4 ***

subtract ** from ***
3x = 9
x = 3, then from ** 6 - y = -5 , y = 11

the original fraction was 3/11

check: (3+5)/(11+5) = 8/16 = 1/2, check!
(3-1)/(11-1) = 2/10 = 1/5, check!

My answer is correct