SOLUTION: given (x) = x / 1-x, show that 1/2 [h(x) + h(-x)] =h(x^2)

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Question 1015436: given (x) = x / 1-x, show that 1/2 [h(x) + h(-x)] =h(x^2)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29+=+x%2F%281-x%29, show that expr%281%2F2%29%28h%28x%29%5E%22%22+%2B+h%28-x%29%29=h%28x%5E2%29

expr%281%2F2%29%28h%28x%29%5E%22%22+%2B+h%28-x%29%29%22%3F=%3F%22h%28x%5E2%29

------------------------------------------------------------

%22%3F=%3F%22x%5E2%2F%281-x%5E2%29

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

expr%281%2F2%29%28%28x%2F%281-x%29%29%5E%22%22+%2B+%28%28-x%29%2F%281%2Bx%29%29%29%22%22=%22%22

%22%22=%22%22

%22%22=%22%22

%22%22=%22%22

expr%281%2F2%29%28%28x%2Bx%5E2-x%2Bx%5E2%29%2F%281-x%5E2%29%29%22%22=%22%22

expr%281%2F2%29%28%282x%5E2%29%2F%281-x%5E2%29%29%22%22=%22%22

expr%281%2Fcross%282%29%29%28%28cross%282%29x%5E2%29%2F%281-x%5E2%29%29%22%22=%22%22

x%5E2%2F%281-x%5E2%29 which was the right side in the first step.

Edwin