The denominator of a fraction is 5 more than twice its numerator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction.

Let the fraction be $x/y.y=2x+5$, and $(x+3)/(y-3)=3/4$ gives $4x+12=3y-9$, that is $4x-3y=-21$. Substituting $y=2x+5:4x-6x-15=-21$, so $-2x=-6$ and $x=3$, giving $y=11$. Check: $11=2\times 3+5$, and 6/8 = 3/4. 3/8 keeps the changed denominator with the original numerator; 6/8 is the changed fraction itself, not the original; 11/3 is the fraction turned upside down.