If x=\frac{4ab}{a+b}, then the value of \frac{x+2a}{x-2a}+\frac{x+2b}{x-2b} is:

Algebra and Applications Test 1

Question : 39 of 40

Marks: +1, -0

x={4ab}/{a+b}

, then the value of

{x+2a}/{x-2a}+{x+2b}/{x-2b}

is:

Solution:

{x+2a}/{x-2a}+{x+2b}/{x-2b}

={2x^2-8ab}/{(x-2a)(x-2b)}

={2( {4ab}/{a+b})^2-8ab}/{( {4ab}/{a+b} -2a)({4ab}/{a+b}-2b)}

={2( {16a^2b^2}/{a^2+b^2+2ab}) -8ab}/{( {4ab-2a^2-2ab}/{a+b} )({4ab-2ab-2b^2}/{a+b} )}

={16a^2b^2-8a^3b-8ab^3}/{8a^2b^2-4a^3b-4ab^3}=2

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