No matter what value X takes, (ax+3)/(bx+5) has a fixed value, so find (A 2+B 2)/(A 2-B 2).

Set the value to k.

(ax+3)/(bx+5)=k

integrate

(kb-a)X=3-5k

If x in this formula is any value.

kb-a=0

And 3-5k=0.

get

The condition is k=3/5.

a=kb=3/5b

Therefore: (A2+B2)/(A2-B2) = (9/2B2+B2)/(9/2B2-B2) =-34/16 =-17/.