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  4. If (1/(3-5x)(2+3x))= (A/3-5x)+ (B/2+3x) then A: B is .................

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Q. If $\frac {1}{(3-5x)(2+3x)}=\frac {A}{3-5x}+ \frac {B}{2+3x}$ then $ A : B $ is .................

KCETKCET 2010Integrals

Solution:

Given, $\frac{1}{(3-5 x)(2+3 x)}=\frac{A}{(3-5 x)}+\frac{B}{(2+3 x)}$
By partial fraction
$1=(3 A-5 B) x+(2 A+3 B)$
On comparing the like powers of ' $x$ '
$3 A-5 B=0$...(i)
and $2 A+3 B=1$...(ii)
On solving, we get $A=\frac{5}{19}, B=\frac{3}{19}$
Hence, $A: B=5: 3$