document.write( "Question 1015790: If b is a positive number and a < b (recall that this is another
\n" ); document.write( "way of saying b-a>0), show that a/b < (a+1)/(b+1) \n" ); document.write( "

Algebra.Com's Answer #632205 by Edwin McCravy(20065) $\"\"$ $\"About$

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document.write( "The other tutor's proof is wrong.  He proved the converse\r\n" );
document.write( "of what you are to prove.  He started by assuming\r\n" );
document.write( "the conclusion and proved what was given.  You must\r\n" );
document.write( "start with what is given, not with what you are to\r\n" );
document.write( "prove.   \r\n" );
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document.write( "Here is the correct proof:\r\n" );
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\n" ); document.write( "If b is a positive number and a < b
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document.write( "We start with what is given,\r\n" );
document.write( "(not with what we are to prove, as he did):\r\n" );
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document.write( "and use the hint:\r\n" );
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document.write( "We replace 0 by the equivalent ab - ab.\r\n" );
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document.write( "We add ab to both sides:\r\n" );
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document.write( "We add a to both sides\r\n" );
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document.write( "Factor out common factors on each side\r\n" );
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document.write( "Divide both sides by b+1, which is positive\r\n" );
document.write( "since b is positive. Therefore we will not \r\n" );
document.write( "reverse the inequality when we divide by b+1:\r\n" );
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document.write( "Divide both sides by b which is positive and\r\n" );
document.write( "also will not reverse the inequality when we \r\n" );
document.write( "divide by it:\r\n" );
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document.write( "which is equivalent to\r\n" );
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document.write( "Edwin

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