Question

resolve into partial fraction​

Answer 1

Answer:

$\frac{a}{ {x}^{2} + 1} + \frac{b}{ {x}^{2} + 2} = \frac{ {x}^{2} }{( {x}^{2} + 1)( {x}^{2} + 2)} \\ \frac{a( {x}^{2} + 2) \: + b( {x}^{2} + 1) }{( {x}^{2} + 1)( {x}^{2} + 2) } = \frac{ {x}^{2} }{( {x}^{2} + 1)( {x}^{2} + 2} \\ ( a {x}^{2} + b {x}^{2} ) + (2a + b) = {x}^{2} \\ a + b = 1 \\ 2a + b = 0 \\ a = - 1 \: \: \: \: \: b = - 2 \\ \frac{ - 1}{ {x}^{2} + 1} + \frac{ - 2}{ {x}^{2} + 2}$