2x x^4 + x^2 + 1 = - Vidyadip

MCQ

${{2x} \over {{x^4} + {x^2} + 1}} = $

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

✓

Answer

Correct option: D.

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

d
(d) ${{2x} \over {{x^4} + {x^2} + 1}} = {{2x} \over {{{({x^2} + 1)}^2} - {x^2}}} = {{2x} \over {({x^2} - x + 1)\,({x^2} + x + 1)}}$

$ = {1 \over {{x^2} - x + 1}} - {1 \over {{x^2} + x + 1}}$.

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