Math
posted by Ghiffari .
The numerator of a fraction is two less than its denominator. When both numerator and denominator are increased by 3, the fraction is incre
ased by 3/20. Find the original fraction. Pls include solution and workings thx :)

first denominator  x
first numerator  x2
new denominator  x+3
new numerator  x+1
(x2)/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
(x5)(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 
Let denominator and numerator be x
The numerator is 2 less than its denominator so
X2/x
It will increased by 3 and will become 3/20 so 
3/5