${{{x^2} - 5} \over {{x^2} - 3x + 2}}$ નું આંશિક અપૂર્ણાક મેળવો.
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d
(d) \({{{x^2} - 5} \over {{x^2} - 3x + 2}} = {{{x^2} - 5} \over {(x - 1)\,(x - 2)}} = {A \over {x - 1}} + {B \over {x - 2}} + C\)
(d) \({{{x^2} - 5} \over {{x^2} - 3x + 2}} = {{{x^2} - 5} \over {(x - 1)\,(x - 2)}} = {A \over {x - 1}} + {B \over {x - 2}} + C\)
\( \Rightarrow \) \({x^2} - 5 = A(x - 2) + B(x - 1) + C(x - 1)(x - 2)\)
\( \Rightarrow \) \(C = 1,\,A + B - 3C = 0,\, - 2A - B + 2C = - 5\)
\(\therefore A = 4,\,B = - 1,\,C = 1\)
\(\therefore \) Given expression = \(1 + {4 \over {x - 1}} - {1 \over {x - 2}}\)
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