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}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $x$ denotes the number of sixes in four consecutive throws of a dice, then $P\,(x = 4)$ is

Which of the following equation is linear

If $\sin \left( {x + \frac{{4\pi }}{9}} \right) = a;\,$ $\frac{\pi }{9}\, < \,x\, < \,\frac{\pi }{3},$ then $\cos \left( {x + \frac{{7\pi }}{9}} \right)$ equals :-

Let $S$ be the infinite sum given by $S=\sum \limits_{n=0}^{\infty} \frac{a_n}{10^{2 n}}$ where $\left(a_n\right)_{n \geq 0}$ is a sequence defined by $a_0=a_1=1$ and $a_j=20 a_{j-1}-108 a_{j-2}$ for $j \geq 2$. If $S$ is expressed in the form $\frac{a}{b}$, where $a, b$ are coprime positive integers, then $a$ equals

The gradient of the tangent line at the point $(a\cos \alpha ,a\sin \alpha )$ to the circle ${x^2} + {y^2} = {a^2}$, is

If $y = f\left( {{{5x + 1} \over {10{x^2} - 3}}} \right)$ and $f'(x) = \cos x$, then ${{dy} \over {dx}} = $

Let $\alpha, \beta$ be two roots of the equation $x^{2}+(20)^{\frac{1}{4}} x+(5)^{\frac{1}{2}}=0$. Then $\alpha^{8}+\beta^{8}$ is equal to:

The straight lines ${I_1},\;{I_2},\;{I_3}$ are parallel and lie in the same plane. A total number of $m$ points are taken on ${I_1},\;n$ points on ${I_2},\;k$ points on ${I_3}$. The maximum number of triangles formed with vertices at these points are

In a $\triangle A B C$, the angle bisector $B D$ of $\angle B$ intersects $A C$ in $D$. Suppose $B C=2, C D=1$ and $B D=\frac{3}{\sqrt{2}}$. The perimeter of the $\triangle A B C$ is

If $M = \left[ {\begin{array}{*{20}{c}}1&2\\2&3\end{array}} \right]$ and ${M^2} - \lambda M - {I_2} = 0$, then $\lambda = $