document.write( "Question 1075937: It is well known that (a/b)+(c/d) is not equivalent to (a+c)/(b+d).
\n" ); document.write( "Suppose that a, b, c, and d are all positive. Show that (a+c)/(b+d) is
\n" ); document.write( "in fact between the numbers a/b and c/d, while (a/b)+(c/d) is not \n" ); document.write( "
Algebra.Com's Answer #690772 by Edwin McCravy(20055)\"\" \"About 
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It is well known that (a/b)+(c/d) is not equivalent to (a+c)/(b+d).
\n" ); document.write( "Suppose that a, b, c, and d are all positive. \r
\n" ); document.write( "\n" ); document.write( "Show that (a+c)/(b+d) is in fact between the numbers a/b and c/d
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document.write( "Case 1.  \"a%2Fb%3C%28a%2Bc%29%2F%28b%2Bd%29\"\r\n" );
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document.write( "Multiply through by LCD b(b+d)\r\n" );
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document.write( "\"a%28b%2Bd%29%3Cb%28a%2Bc%29\"\r\n" );
document.write( "\"ab%2Bad%3Cab%2Bbc\"\r\n" );
document.write( "Subtract ab from both sides\r\n" );
document.write( "\"ad%3Cbc\"\r\n" );
document.write( "Add cd to both sides\r\n" );
document.write( "\"ad%2Bcd%3Cbc%2Bcd\"\r\n" );
document.write( "Factor out d on left, c on right\r\n" );
document.write( "\"d%28a%2Bc%29%3Cc%28b%2Bd%29\"\r\n" );
document.write( "Divide both sides by d(b+d)\r\n" );
document.write( "\"%28a%2Bc%29%2F%28b%2Bd%29%3Cc%2Fd\"\r\n" );
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document.write( "So \"a%2Fb%3C%28a%2Bc%29%2F%28b%2Bd%29%3Cc%2Fd\"\r\n" );
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document.write( "Case 2.  \"a%2Fb%3E%28a%2Bc%29%2F%28b%2Bd%29\"\r\n" );
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document.write( "Multiply through by LCD b(b+d)\r\n" );
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document.write( "\"a%28b%2Bd%29%3Eb%28a%2Bc%29\"\r\n" );
document.write( "\"ab%2Bad%3Eab%2Bbc\"\r\n" );
document.write( "Subtract ab from both sides\r\n" );
document.write( "\"ad%3Ebc\"\r\n" );
document.write( "Add cd to both sides\r\n" );
document.write( "\"ad%2Bcd%3Ebc%2Bcd\"\r\n" );
document.write( "Factor out d on left, c on right\r\n" );
document.write( "\"d%28a%2Bc%29%3Ec%28b%2Bd%29\"\r\n" );
document.write( "Divide both sides by d(b+d)\r\n" );
document.write( "\"%28a%2Bc%29%2F%28b%2Bd%29%3Ec%2Fd\"\r\n" );
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document.write( "So \"a%2Fb%3E%28a%2Bc%29%2F%28b%2Bd%29%3Ec%2Fd\"\r\n" );
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document.write( "In either case, \"%28a%2Bc%29%2F%28b%2Bd%29\" is between \"a%2Fb\" and \"c%2Fd\"\r\n" );
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document.write( "---------------------------------\r\n" );
document.write( "  \r\n" );
document.write( "\"a%2Fb%2Bc%2Fd\" is not between the numbers \"a%2Fb\" and \"c%2Fd\"\r\n" );
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document.write( "because the sum of two positive numbers is greater than\r\n" );
document.write( "either one.\r\n" );
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document.write( "Edwin
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