Mathematics

Partial fraction from of $$\displaystyle \frac{3x+7}{x^2-3x+2}$$ is 


ANSWER

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


SOLUTION
Let $$\displaystyle \frac { 3x+7 }{ x^{ 2 }-3x+2 } =\frac { A }{ \left( x-2 \right)  } +\frac { B }{ \left( x-1 \right)  } $$
$$\Rightarrow 3x+7=A\left( x-1 \right) +B\left( x-2 \right) $$
On comparing coefficients $$3=A+B,7=-A-2B\Rightarrow A=13,B=-10$$
Thus
$$\displaystyle \frac { 3x+7 }{ x^{ 2 }-3x+2 } =\frac { 13 }{ \left( x-2 \right)  } -\frac { 10 }{ \left( x-1 \right)  } $$
Hence, option 'A' is correct.
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Single Correct Medium Published on 17th 09, 2020
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