document.write( "Question 1083841: If b is the harmonic mean between a and c,then prove that:1/(b-a) +1/(b-c)=1/a+1/c \n" ); document.write( "
Algebra.Com's Answer #697967 by Edwin McCravy(20056)\"\" \"About 
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document.write( "We find the arithmetic mean of \"1%2Fa\" and \"1%2Fc\"\r\n" );
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document.write( "Add them \"1%2Fa%2B1%2Fc=%28a%2Bc%29%2F%28ac%29\"\r\n" );
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document.write( "Divide by 2:  \"%28a%2Bc%29%2F%282ac%29\"\r\n" );
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document.write( "Its reciprocal \"%282ac%29%2F%28a%2Bc%29\" is the harmonic mean\r\n" );
document.write( "between a and c, so\r\n" );
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document.write( "\"b=%282ac%29%2F%28a%2Bc%29\"\r\n" );
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document.write( "Substitute for b in\r\n" );
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document.write( "\"1%2F%28b-a%29+%2B1%2F%28b-c%29\"\r\n" );
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document.write( "\"1%2F%28%28%282ac%29%2F%28a%2Bc%29%29-a%29+%2B1%2F%28%28%282ac%29%2F%28a%2Bc%29%29-c%29\"\r\n" );
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document.write( "Multiply numerators and denominators by (a+c)\r\n" );
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document.write( "\"%28a%2Bc%29%2F%282ac-a%28a%2Bc%29%29+%2B%28a%2Bc%29%2F%282ac-c%28a%2Bc%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%282ac-a%5E2-ac%29+%2B%28a%2Bc%29%2F%282ac-ac-c%5E2%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%28ac-a%5E2%29+%2B%28a%2Bc%29%2F%28ac-c%5E2%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%28a%28c-a%29%29+%2B%28a%2Bc%29%2F%28c%28a-c%29%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%28a%28c-a%29%29+%2B%28a%2Bc%29%2F%28c%28-c%2Ba%29%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%28a%28c-a%29%29+%2B%28a%2Bc%29%2F%28-c%28c-a%29%29%29\"\r\n" );
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document.write( "\"%28a%2Bc%29%2F%28a%28c-a%29%29+-%28a%2Bc%29%2F%28c%28c-a%29%29%29\"\r\n" );
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document.write( "Factor out \"%28a%2Bc%29%2F%28c-a%29\"\r\n" );
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document.write( "\"%28%28a%2Bc%29%2F%28c-a%29%29%281%2Fa-1%2Fc%29%29%29\"\r\n" );
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document.write( "\"%28%28a%2Bc%29%2F%28c-a%29%29%28%28c-a%29%2F%28ac%29%29%29%29\"\r\n" );
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document.write( "\"%28%28a%2Bc%29%2F%28cross%28c-a%29%29%29%28%28cross%28c-a%29%29%2F%28ac%29%29%29%29\"\r\n" );
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document.write( "\"%28%28a%2Bc%29%2F%28ac%29%29%29%29\"\r\n" );
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document.write( "\"a%2F%28ac%29%2Bc%2F%28ac%29\"\r\n" );
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document.write( "\"cross%28a%29%2F%28cross%28a%29c%29%2Bcross%28c%29%2F%28a%2Across%28c%29%29\"\r\n" );
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document.write( "\"1%2Fc%2B1%2Fa\"\r\n" );
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document.write( "\"1%2Fa%2B1%2Fc\"\r\n" );
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document.write( "Edwin
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