Q84 / 180 · KCET 2010 · Mathematics

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

  • A
    $2: 3$
  • Correct answer
    B
    $5: 3$
  • C
    $3: 5$
  • D
    $3: 2$

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 ' $x$ ' and $\quad \begin{array}{rr}3 A-5 B=0 & \ldots \text { (i) } \\ 2 A+3 B=1 & \ldots \text { (ii) }\end{array}$ On solving, we get $\mathrm{A}=\frac{5}{19}, \mathrm{~B}=\frac{3}{19}$ Hence, $\quad \mathrm{A}: \mathrm{B}=5: 3$

Hence, the correct answer is option: 'B'.

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