Simplify the following expression- 1-2 - 2 -a - 1-2 - 2 -a - a2 - 1-1 - a2 1 - 1-a

( 1 2+2√( a ) #160; + 1 2 2√( a ) #160; a ^ 2 +1 1 a ^ 2 #160; ) ( 1+ 1 a #160; ) ⇒[ 1 2+2√( a ) #160; ( 2 2√( a ) #160; ) ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (x^2 - y^2)

Simplify the ...

Question

Simplify the following expression:
$(\frac{1}{2 + 2 \sqrt{a}} + \frac{1}{2 - 2 \sqrt{a}} - \frac{a^{2} + 1}{1 - a^{2}}) (1 + \frac{1}{a})$

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Solution

$(\frac{1}{2 + 2 \sqrt{a}} + \frac{1}{2 - 2 \sqrt{a}} - \frac{a^{2} + 1}{1 - a^{2}}) (1 + \frac{1}{a})$

$\Rightarrow [\frac{1}{2 + 2 \sqrt{a}} \frac{(2 - 2 \sqrt{a})}{(2 - 2 \sqrt{a})} + \frac{1}{2 - 2 \sqrt{a}} \frac{(2 + 2 \sqrt{a})}{(2 + 2 \sqrt{a})} - (\frac{a^{2} + 1}{1 - a^{2}})] (1 + \frac{1}{a})$

$\Rightarrow (\frac{2 - 2 \sqrt{a} + 2 + 2 \sqrt{a}}{4 - 4 a} - (\frac{a^{2} + 1}{1 - a^{2}})) (1 + \frac{1}{a})$

$\Rightarrow (\frac{1}{1 - a}) - (\frac{1 + a^{2}}{(1 - a) (1 + a)}) (\frac{(1 + a)}{a})$

$\Rightarrow \frac{(1 + a) - 1 - a^{2}}{(1 - a) (1 + a)} \frac{(1 + a)}{a}$

$\Rightarrow \frac{a - a^{2}}{a - a^{2}} = 1.$
Hence, the answer is $1.$

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Simplify the following expression:(12+2√a+12−2√a−a2+11−a2)(1+1a)

(12+2√a+12−2√a−a2+11−a2)(1+1a)⇒[12+2√a(2−2√a)(2−2√a)+12−2√a(2+2√a)(2+2√a)−(a2+11−a2)](1+1a)⇒(2−2√a+2+2√a4−4a−(a2+11−a2))(1+1a)⇒(11−a)−(1+a2(1−a)(1+a))((1+a)a)⇒(1+a)−1−a2(1−a)(1+a)(1+a)a⇒a−a2a−a2=1.Hence, the answer is 1.

Simplify the following expression:
$(\frac{1}{2 + 2 \sqrt{a}} + \frac{1}{2 - 2 \sqrt{a}} - \frac{a^{2} + 1}{1 - a^{2}}) (1 + \frac{1}{a})$