SSC CHSL 15 Nov 2015 Shift 1 Paper

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Question : 146 of 199

Marks: +1, -0

If

{x+1}/{x−1 }= a/b

and

{1−y}/{1+y }= b/ a

, then the value of

{x−y}/{1+xy}

is:

${a ^2−b^2}/{2ab }$
${a ^2+b^2}/{2ab }$
${2ab }/{a ^2-b^2}$
${a ^2+b^2}/{ab }$

Solution:

Given :

{x+1}/{x−1 }= a/b

⇒

b(x + 1) = a(x − 1)

⇒

bx + b = ax − a

⇒

x(a − b) = a + b

⇒

x = {a+b}/{a−b}

Similarly,

y={a-b}/{a+b}

To find :

{x−y}/{1+xy}

=

[({a+b }/{ a−b }) − ({a−b}/ {a+b} )]

÷ [1 + ( {a+b}/{a−b} )({a−b}/ {a+b})]

=

({ (a+b)^2-(a−b) ^2}/{(a+b)(a−b)}) ÷ (1 + 1)

=

{(a^2 +b^2 +2ab)−(a^2 +b^2 −2ab)}/ {a^2-b^2}

×(1/2)

=

{4ab}/{2(a^2 −b^2 )}

=

{2ab }/{a ^2-b^2}

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