document.write( "Question 544837: I need help finding 2 consecutive natural numbers such that the difference of their reciprocals is 1/4 the reciprocal of the smaller number. \n" ); document.write( "

Algebra.Com's Answer #355249 by friesr(113) $\"\"$ $\"About$

You can put this solution on YOUR website!
x
\n" ); document.write( "x + 1 = \r
\n" ); document.write( "\n" ); document.write( " $\"1%2F%28x%2B1%29-+1%2Fx+=+1%2Fx+%2A+1%2F4\"$
\n" ); document.write( "Lets get a commone denominator:
\n" ); document.write( " $\"+x%2F%28x%28x%2B1%29%29+-+%28x%2B1%29%2F%28x%28x%2B1%29%29+=+1%2F4x\"$
\n" ); document.write( "-
\n" ); document.write( " $\"+x-x%2B1+%2F+x%28x%2B1%29+=+1%2F4x\"$
\n" ); document.write( "-
\n" ); document.write( " $\"1%2Fx%28x%2B1%29+=+1%2F%284x%29\"$
\n" ); document.write( "-
\n" ); document.write( "Multiply both sides by x
\n" ); document.write( " $\"1%2F%28x%2B1%29+=+1%2F4\"$
\n" ); document.write( "-
\n" ); document.write( " $\"x%2B1+=+4\"$
\n" ); document.write( "--
\n" ); document.write( "x=3
\n" ); document.write( "===
\n" ); document.write( "Your numbers are 3 and 4
\n" ); document.write( "--
\n" ); document.write( "Check:
\n" ); document.write( "1/3 - 1/4 = 1/4 * 1/3
\n" ); document.write( "-
\n" ); document.write( "4/12 - 3/12 = 1/12
\n" ); document.write( "1/12 = 1/12
\n" ); document.write( " \n" ); document.write( "

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