document.write( "Question 736937: The sum of the reciprocal of a number and the reciprocal of 3 less than the number is 6 times the reciprocal of the original number. Find the original number \n" ); document.write( "
Algebra.Com's Answer #450258 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The sum of the reciprocal of a number and the reciprocal of 3 less than the number is 6 times the reciprocal of the original number.
\n" ); document.write( " Find the original number
\n" ); document.write( ":
\n" ); document.write( "let n = original number
\n" ); document.write( ":
\n" ); document.write( "\"1%2Fn\" + \"1%2F%28%28n-3%29%29\" = \"6%2Fn\"
\n" ); document.write( "multiply by n(n-3), resulting in
\n" ); document.write( "(n-3) + n = 6(n-3)
\n" ); document.write( "n - 3 + n = 6n - 18
\n" ); document.write( "2n - 6n = -18 + 3
\n" ); document.write( "-4n = -15
\n" ); document.write( "n = -15/-4
\n" ); document.write( "n = +3.75 is the original number
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Expected an integer here, see if this checks out:
\n" ); document.write( "\"1%2F3.75\" + \"1%2F.75\" = \"6%2F3.75\"
\n" ); document.write( ".267 + 1.333 = 1.6, it does! \n" ); document.write( "
\n" );