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

More "MCQ" from basic of algoritham→basic of algoritham — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If ${^\text{n}}\text{C}_{\text{12}}={^\text{n}}\text{C}_{\text{8}},$ is then n:

Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is

If ${( - 7 - 24i)^{1/2}} = x - iy,$ then ${x^2} + {y^2} = $

The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ resepectively. Each of these $10$ observations is multiplied by $\mathrm{p}$ and then reduced by $\mathrm{q}$, where $\mathrm{p} \neq 0$ and $\mathrm{q} \neq 0 .$ If the new mean and new s.d. become half of their original values, then $q$ is equal to

The $4^{th}$ term in the expansion of $\Big(\sqrt{\text{x}}+\frac{1}{\text{x}}\Big)^{12}$ is:

Choose the correct statement which describe the position of the point $(-6, 2)$ relative to straight lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$

$\mathop {\lim }\limits_{x \to 0} $ $\frac{{\int\limits_0^x ( {\text{ta}}{{\text{n}}^{ - 1}}{\text{ t }}{{\text{)}}^2}{\text{dt}}}}{{({\text{sinx - x}})}}$ is-

Let $f:R \to R$ be a differentiable function having $f(2) = 6,f'(2) = \left( {\frac{1}{{48}}} \right).$ Then $\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f(x)} {\frac{{4{t^3}}}{{x - 2}}} dt$ equals

Out of $40$ consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$

$2.$ Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

$(A)$ $2 x-\sqrt{5} y-20=0$ $(B)$ $2 x-\sqrt{5} y+4=0$

$(C)$ $3 x-4 y+8=0$ $(D)$ $4 x-3 y+4=0$

$2.$ Equation of the circle with $\mathrm{AB}$ as its diameter is

$(A)$ $x^2+y^2-12 x+24=0$ $(B)$ $x^2+y^2+12 x+24=0$

$(C)$ $\mathrm{x}^2+\mathrm{y}^2+24 \mathrm{x}-12=0$ $(D)$ $x^2+y^2-24 x-12=0$

Give hte answer question $1, 2$