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Q. Multiplicative inverse of

Real Numbers

Solution:

Cognitive Level: HM
Let $x =a+2+\frac{4}{a-2} $
$ =\frac{(a+2)(a-2)+4}{a-2}$
$ =\frac{a^2-4+4}{a-2}\left[\mathrm{As},(a+b)(a-b)=a^2-b^2\right]$
$\therefore x =\frac{a^2}{a-2}$
Multiplicative inverse of
$x =\frac{1}{x} $
$ =\frac{1}{\frac{a^2}{a-2}} $
$ =\frac{a-2}{a^2}$