Q59 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

If $\frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6}$ then $A+B=$

  • Correct answer
    A
    $8$
  • B
    $18$
  • C
    $3$
  • D
    $5$

Solution

$\begin{aligned} & \frac{13 x+43}{2 x^2+17 x+30}=\frac{\mathrm{A}}{2 x+5}+\frac{\mathrm{B}}{x+6} \\ & \frac{13 x+43}{2 x^2+17 x+30}=\frac{\mathrm{A}(x+6)+\mathrm{B}(2 x+5)}{2 x^2+17 x+30} \\ & \Rightarrow 13 x+43=\mathrm{A}(x+6)+\mathrm{B}(2 x+5) \\ & \Rightarrow 13 x+43=(\mathrm{A}+2 \mathrm{~B}) x+6 \mathrm{~A}+5 \mathrm{~B}\end{aligned}$ On comparing, $\mathrm{A}+2 \mathrm{~B}=13$ ...(i) $6 A+5 B=43$ ...(ii) On solving (i) and (ii) we get $A=3, B=5 \Rightarrow A+B=8$

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

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