Mathematics

# $\dfrac{3x+7}{x^{2}-3x+2}=$

$\displaystyle \frac{13}{x-2}-\frac{10}{x-1}$

##### SOLUTION
Reduction into partial dfractions write the
$D(x)=(ax+b)(cx+d)$

factorizing $x^{2}-3x+2$ we get $(x-1)(x-2)$

So, $\dfrac{3x+7}{(x-1)(x-2)}=\dfrac{A}{x-1}+\dfrac{B}{x-2} --1)$

$3x+7=A(x-2)+B(x-1) --(2)$  from the eqn (1)

So, let $x=2$ in the equation (2)

we get $13=B$ and
let $x=1$ in the equation
$A=-10$

So, $\dfrac{-10}{x-1}+\dfrac{13}{x-2}=\dfrac{13}{x-2}-\dfrac{10}{x-1}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

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