Mathematics

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


ANSWER

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


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
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