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Modulus of a Complex Number

x2+5/x2+22=1/...

Question

$\frac{x^{2} + 5}{(x^{2} + 2)^{2}} = \frac{1}{x^{2} + 2} + \frac{k}{(x^{2} + 2)^{2}} \Rightarrow k =$

A

1

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B

2

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C

3

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D

5

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Solution

The correct option is C $3$
$L H S = \frac{x^{2} + 5}{(x^{2} + 2)^{2}}; R H S = \frac{1}{x^{2} + 2} + \frac{k}{(x^{2} + 2)^{2}}$
$= \frac{(x^{2} + 2) + k 1}{(x^{2} + 2)^{2}}$
$L H S = R H S$
$\frac{x^{2} + 5}{(x^{2} + 2)^{2}} = \frac{x^{2} + 2 + k}{(x^{2} + 2)^{2}}$
$x^{2} + 5 = x^{2} + 2 + 1$
$2 + k = 5$
$k = 3$

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