document.write( "Question 1015436: given (x) = x / 1-x, show that 1/2 [h(x) + h(-x)] =h(x^2) \n" ); document.write( "
Algebra.Com's Answer #631801 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"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\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28h%28x%29%5E%22%22+%2B+h%28-x%29%29\"\"%22%3F=%3F%22\"\"h%28x%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------------------------\r\n" );
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document.write( "\"%22%3F=%3F%22\"\"x%5E2%2F%281-x%5E2%29\"\r\n" );
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document.write( "We work with the left side and show that it equals the right side:\r\n" );
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document.write( "\"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\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28%28x%2Bx%5E2-x%2Bx%5E2%29%2F%281-x%5E2%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2F2%29%28%282x%5E2%29%2F%281-x%5E2%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"expr%281%2Fcross%282%29%29%28%28cross%282%29x%5E2%29%2F%281-x%5E2%29%29\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2F%281-x%5E2%29\" which was the right side in the first step.\r\n" );
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document.write( "Edwin
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