The correct option is A 1/x^2+1+22/(x^2+1)^2+5/(x^2+1)^3 solving through substitution method x^2+1=k⇒ x^2=k 1 substituting in the question equation ...

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Definition of Functions

x4+24x2+28/x2...

Question

$\frac{x^{4} + 24 x^{2} + 28}{(x^{2} + 1)^{3}} =$

\frac{1}{x^{2} + 1} + \frac{22}{(x^{2} + 1)^{2}} + \frac{5}{(x^{2} + 1)^{3}}

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\frac{1}{x^{2} + 1} - \frac{22}{(x^{2} + 1)^{2}} + \frac{5}{(x^{2} + 1)^{3}}

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\frac{1}{x^{2} + 1} + \frac{22}{(x^{2} + 1)^{2}} + \frac{28}{(x^{2} + 1)^{3}}

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\frac{1}{x^{2} + 1} + \frac{23}{(x^{2} + 1)^{2}} + \frac{4}{(x^{2} + 1)^{3}}

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Solution

The correct option is A $\frac{1}{x^{2} + 1} + \frac{22}{(x^{2} + 1)^{2}} + \frac{5}{(x^{2} + 1)^{3}}$
solving through substitution method

$x^{2} + 1 = k \Rightarrow x^{2} = k - 1$

substituting in the question equation

$\frac{(k - 1)^{2} + 24 (k - 1) + 28}{k^{3}} = \frac{k^{2} + 22 k + 5}{k^{3}}$

$= \frac{1}{k} + \frac{22}{k^{2}} + \frac{5}{k^{3}}$

$= \frac{1}{(x^{2} + 1)} + \frac{22}{(x^{2} + 1)^{2}} + \frac{5}{(x^{2} + 1)^{3}}$ [we know that $k = x^{2} + 1$ ]

$\frac{x^{4} + 24 x^{2} + 28}{(x^{2} + 1)^{3}} = \frac{1}{(x^{2} + 1)} + \frac{22}{(x^{2} + 1)^{2}} + \frac{5}{(x^{2} + 1)^{3}}$

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Similar questions

Q. If

\frac{x^{4} + 24 x^{2} + 28}{(x^{2} + 1)^{3}}

= \frac{A x + B}{x^{2} + 1} + \frac{C x + D}{(x^{2} + 1)^{2}} + \frac{E x + F}{(x^{2} + 1)^{3}}

then

A =

\frac{3 x^{2} + 1}{(x^{2} + 1)^{3}} = \frac{A x + B}{(x^{2} + 1)} + \frac{C x + D}{(x^{2} + 1)^{2}} + \frac{E x + F}{(x^{2} + 1)^{3}}

then

A + C + E + F =

Q. Factorise

x^{2} - \frac{13}{24} x - \frac{1}{12}

Q. Differentiate

{cot}^{- 1} \frac{2 \sqrt{1 + x^{2}} - 5 \sqrt{1 - x^{2}}}{5 \sqrt{1 + x^{2}} + 2 \sqrt{1 - x^{2}}}

with respect to

{cos}^{- 1} \sqrt{(1 - x^{4})} .

\frac{x^{4} - 5 x^{2} + 1}{(x^{2} + 1)^{3}} =

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x4+24x2+28(x2+1)3=

The correct option is A 1x2+1+22(x2+1)2+5(x2+1)3solving through substitution methodx2+1=k⇒x2=k−1substituting in the question equation(k−1)2+24(k−1)+28k3=k2+22k+5k3=1k+22k2+5k3=1(x2+1)+22(x2+1)2+5(x2+1)3 [we know that k=x2+1]x4+24x2+28(x2+1)3=1(x2+1)+22(x2+1)2+5(x2+1)3

$\frac{x^{4} + 24 x^{2} + 28}{(x^{2} + 1)^{3}} =$