The partial fractions of x^2 - 5 x^2 - 3x + 2 are - Vidyadip

MCQ

The partial fractions of ${{{x^2} - 5} \over {{x^2} - 3x + 2}}$ are

A
$1 + {1 \over {(x - 1)}} - {1 \over {{{(x - 2)}^2}}}$
B
${1 \over {(x - 1)}} + {1 \over {{{(x - 2)}^2}}}$
C
${1 \over {(x - 1)}} - {1 \over {{{(x - 2)}^2}}}$
✓
$1 + {4 \over {(x - 1)}} - {1 \over {(x - 2)}}$

✓

Answer

Correct option: D.

$1 + {4 \over {(x - 1)}} - {1 \over {(x - 2)}}$

d
(d) ${{{x^2} - 5} \over {{x^2} - 3x + 2}} = {{{x^2} - 5} \over {(x - 1)\,(x - 2)}} = {A \over {x - 1}} + {B \over {x - 2}} + C$

$ \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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