The simplified value of (1- {2 x y}/{x^{2}+y^{2}} )\div ( {x^{3}-y^{3}}/{x-y}-3 x y ) is

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 66 of 100

Marks: +1, -0

The simplified value of

(1- {2 x y}/{x^{2}+y^{2}} )÷ ( {x^{3}-y^{3}}/{x-y}-3 x y )

Solution:

(2) Expression

= (1- {2 x y}/{x^{2}+y^{2}} )÷ ( {x^{3}-y^{3}}/{x-y}-3 x y )

= ( {x^{2}+y^{2}-2 x y}/{x^{2}+y^{2}} ) ÷( {(x-y) (x^{2}+x y+y^{2} )}/{x-y}-3 x y )

= {(x-y)^{2}}/{x^{2}+y^{2}}÷(x^{2}+x y+y^{2}- 3 x y )

= {(x-y)^{2}}/{x^{2}+y^{2}} ÷(x^{2}-2 x y+y^{2} )

= {(x-y)^{2}}/{x^{2}+y^{2}} ÷(x-y)^{2}= {1}/{x^{2}+y^{2}}

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