The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with 1/2. Find the fraction.

let the numerator be x, so dthe enominator is x + 12

New numerator is x – 2 , newthe denominator is x + 12 + 7

So according to given conditions

Multiplying both sides by

Multiplying by x + 19 on both sides

2(x – 2) = x + 19

2x – 4 = x + 19

Adding – x on both sides

x – 4 = 19

Adding 4 on both sides

x = 23

So, numerator is 23 and denominator is 12 + 23 = 35

Required fraction is