Let the numerator be x
Therefore, denominator is x+2
The fraction is xx+2
Now, xx+2+x+1x+3=1915
=>x2+3x+(x+1)(x+2)(x+2)(x+3)=1915
=>x2+3x+x2+3x+2(x+2)(x+3)=1915
=>15(x2+3x+x2+3x+2)=19(x+2)(x+3)
=>15(2x2+6x+2)=19(x2+5x+6)
=>30x2+90x+30=19x2+95x+114
=>11x2−5x−84=0
=>11x2−33x+28x−84=0
=>11x(x−3)+28(x−3)=0
=>(11x+28)(x−3)=0
Therefore, x=3 or x=−2811
For x=−2811, denominator is :-
−2811+2=−28+2211=−611
So, the fraction is −2811−611=286=143
Now adding 1 on both numerator and denominator we get 154
But, 143+154≠1915
∴x=3 and denominator is x+2=3+2=5
∴ the fraction is 35