document.write( "Question 1044351: The sum of the reciprocals of two consecutive integers is equal to 11 times the reciprocal of the product of those integers.what are the two integers? \n" ); document.write( "
Algebra.Com's Answer #659617 by KMST(5328)\"\" \"About 
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Let's say that
\n" ); document.write( "\"n\"= one of the integers involved, with \"n%3C%3E0\" , so that the reciprocal of \"n\" exists.
\n" ); document.write( "\"1%2Fn\"= the reciprocal of the integer above.
\n" ); document.write( "For consecutive integers, let's say that
\n" ); document.write( "\"n%2B1\"= the other integer, also with \"n%2B1%3C%3E0\" , so
\n" ); document.write( "\"1%2F%28n%2B1%29\"= the reciprocal of the \"other integer\" above.
\n" ); document.write( "So, \"n%28n%2B1%29\"= the product of those integers.
\n" ); document.write( "Since neither \"n\" , nor \"n%2B1\" is zero,
\n" ); document.write( "neither is their product: \"n%28n%2B1%29%3C%3E0\" ,so the reciprocal exists.
\n" ); document.write( "\"1%2F%28n%28n%2B1%29%29\"= the reciprocal of the product of those two consecutive integers.
\n" ); document.write( "What the problem says is that
\n" ); document.write( "\"1%2Fn%2B1%2F%28n%2B1%29=11%281%2F%28n%28n%2B1%29%29%29\"
\n" ); document.write( "That is the equation to simplify and solve.
\n" ); document.write( "\"1%2Fn%2B1%2F%28n%2B1%29=11%281%2F%28n%28n%2B1%29%29%29\"
\n" ); document.write( "\"%28n%2B1%29%2F%28n%28n%2B1%29%29%2Bn%2F%28n%28n%2B1%29%29=11%2F%28n%28n%2B1%29%29\"
\n" ); document.write( "\"%28n%2Bn%2B1%29%2F%28n%28n%2B1%29%29=11%2F%28n%28n%2B1%29%29\"
\n" ); document.write( "\"%282n%2B1%29%2F%28n%28n%2B1%29%29=11%2F%28n%28n%2B1%29%29\"
\n" ); document.write( "Since \"n%28n%2B1%29%3E0\" , we can multiply both sides of the equation times \"n%28n%2B1%29\" to get a simpler, equivalent equation.
\n" ); document.write( "\"2n%2B1=11\"
\n" ); document.write( "\"2n=11-1\"
\n" ); document.write( "\"2n=10\"
\n" ); document.write( "\"n=10%2F2\"
\n" ); document.write( "\"highlight%28n=5%29\"
\n" ); document.write( "\"n%2B1=5%2B1\"
\n" ); document.write( "\"highlight%28n%2B1=6%29\"
\n" ); document.write( "The two integers are \"highlight%285%29\" and \"highlight%286%29\" . \n" ); document.write( "
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