x + 1 (x - 1) ,(x - 2) ,(x - 3) = - Vidyadip

MCQ

${{x + 1} \over {(x - 1)\,(x - 2)\,(x - 3)}} = $

A
${1 \over {x - 1}} + {3 \over {x - 2}} + {1 \over {x - 3}}$
B
$ - {3 \over {x - 1}} + {1 \over {x - 2}} + {2 \over {x - 3}}$
✓
${1 \over {x - 1}} - {3 \over {x - 2}} + {2 \over {x - 3}}$
D
None of these

✓

Answer

Correct option: C.

${1 \over {x - 1}} - {3 \over {x - 2}} + {2 \over {x - 3}}$

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

$ \Rightarrow $$x + 1 = A\,(x - 2)\,(x - 3)\, + B(x - 1)\,(x - 3) + C(x - 1)\,(x - 2)$

Putting $x = 1,\,A = 1$ ; $x=2$ gives $B = - 3$,

For $x = 3,\,C = 2$

$\therefore$ Given expression = ${1 \over {x - 1}} - {3 \over {x - 2}} + {2 \over {x - 3}}$.

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