solving equations with ratical expression

Question

If the same number is subtracted from both the numerator and the denominator of 1117, the result is 47. Find the number.

Answer 1

11/17 becomes 4/7 when

(11-x)/(17-x) = 4/7

cross multiply

77 -7x = 68 -4x

7x-4x = 77-68

3x= 9

x= 2

subtract 3 from both numerator 11 and denominator 17 and it becomes 4/7

11- 3= 8

17-3 = 14

8/14 = 4/7