Question 1015436
<pre>
{{{h(x) = x/(1-x)}}}, show that {{{expr(1/2)(h(x)^"" + h(-x))=h(x^2)}}}

{{{expr(1/2)(h(x)^"" + h(-x))}}}{{{"?=?"}}}{{{h(x^2)}}}

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{{{expr(1/2)((x/(1-x))^"" + (((-x))/(1-(-x))))}}}{{{"?=?"}}}{{{x^2/(1-x^2)}}}

We work with the left side and show that it equals the right side:

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

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

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

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

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

{{{expr(1/2)((2x^2)/(1-x^2))}}}{{{""=""}}}

{{{expr(1/cross(2))((cross(2)x^2)/(1-x^2))}}}{{{""=""}}}

{{{x^2/(1-x^2)}}} which was the right side in the first step.

Edwin</pre>