Question 1015396
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If y(x) = x / 1-x , show that 1/2 [y(x) + y(-x)] = y(x^2)
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y(x) = {{{x/(1-x)}}},

y(-x) = {{{(-x)/(1-(-x))}}} = {{{-x/(1+x)}}}.

Therefore, 

y(x) + y(-x) = {{{x/(1-x)}}} - {{{x/(1+x)}}} =    (now write it with the common denominator, which is (1-x)*(1+x) )

= {{{(x*(1+x))/((1-x)*(1+x))}}} - {{{(x*(1-x))/((1-x)*(1+x))}}} = 

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

Therefore, 

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

It is what has to be proved.
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