Mathematics

# If $\displaystyle \frac{3x+4}{x^2-3x+2}=\frac{A}{x-2}-\frac{B}{x-1}$, then $(A,B)$=

$(10, 7)$

##### SOLUTION
$\displaystyle \frac{3x+4}{x^2-3x+2}=\frac{A}{x-2}-\frac{B}{x-1}$            ....(1)

Consider,$\displaystyle \frac { 3x+4 }{ x^{ 2 }-3x+2 }$
Resolving into partial fractions
$\displaystyle \frac { 3x+4 }{ (x-1)(x-2) } =\frac { A }{ x-2 } +\frac { B }{ x-1 }$     ....(2)
$3x+4=A(x-1)+B(x-2)$
$3x+4=(A+B)x+(-A-2B)$
$\Rightarrow A+B=3,-A-2B=4$
Solving these equations, we get
$B=-7, A=10$
Put these values in (2)
$\displaystyle \frac { 3x+4 }{ (x-1)(x-2) } =\frac { 10 }{ x-2 } -\frac { 7 }{ x-1 }$
Comparing this with (1), we get
$(A,B) = (10,7)$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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