Question

the numerator of a fraction is 2 less than its denominator. when both numerator and denominator are increased by 3, the fraction is increased by 3/20. find the original fraction

Answer 1

First denominator -- x 
first numerator ---- x-2 

new denominator -- x+3 
new numerator ---- x+1 

(x-2)/x + 3/20 = (x+1)/(x+3) 
times 20x(x+3) , the LCD 
20(x+3)(x+1) + 3x(x+3) = 20x(x+1) 
expanding and simplifying gave me 
x^2 + 3x - 40 = 0 
(x-5)(x+8) = 0 
x = 5 or x=-8 

if x=5, the original fraction was 3/5 
if x=-8 the original fraction was -10/-8 or 5/4 

check for 3/5 , new fraction would be 6/8 or 3/4 
3/5 + 3/20 = 12/20 + 3/20 = 15/20 = 3/4 

but for 5/4, new fraction would be 8/7 
5/4 + 3/20 = 28/20 = 7/5 ≠ 8/7 
BUT, if we take the unsimplified fraction -10/-8 , new fraction would be -7/-5 = 7/5 

So the original fraction would be 3/5 for sure, but 
also the unsimplified fraction -10/-8

Answer 2

The original fraction will be 3/5 and I am positive. :D