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CDS Model Paper 2 Mathematics

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Question : 31 of 100

Marks: +1, -0

If

x=\frac{4ab}{a+b}

, then the value of

\frac{x+2a}{x-2a}

\div

\frac{x+2b}{x-2b}

0
1
2
None of these

Solution:

Given,

x=\frac{4ab}{a+b}

⇒

\frac{x}{2a}=\frac{2b}{a+b}

Applying componendo and dividendo, we get

\frac{x+2a}{x-2a}=\frac{2b+a+b}{2b-a-b}=\frac{a+3b}{b-a}

...(i)

Also,

\frac{x}{2b}=\frac{2a}{a+b}

Applying componendo and dividendo, we get

\frac{x+2b}{x-2b}=\frac{2a+a+b}{2a-a-b}=\frac{3a+b}{a-b}

...(ii)

Add (i) & (ii),

\frac{x+2a}{x-2a}+\frac{x+2b}{x-2b}=\frac{a+3b}{b-a}+\frac{3a+b}{a-b}

=\frac{1}{b-a}[a+3b-3a-b]=\frac{2(b-a)}{b-a}=2

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