document.write( "Question 230130: The denominator of a fraction is an integer that is 4 more than the square of the numerator. if the fraction is reduced to lowest terms, it equals 3/20. find the numerator \n" ); document.write( "

Algebra.Com's Answer #170805 by jsmallt9(3758) $\"\"$ $\"About$

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$\"x%2F%284%2Bx%5E2%29+=+3%2F20\"$
\n" ); document.write( "To get rid of the fractions we will multiply by the Lowest Common Denominator (LCD). The LCD here is: 20(4+x^2).
\n" ); document.write( " $\"20%284%2Bx%5E2%29%28x%2F%284%2Bx%5E2%29%29+=+20%284%2Bx%5E2%29%283%2F20%29\"$
\n" ); document.write( "Cancel common factors on each side:
\n" ); document.write( "

\n" ); document.write( "leaving:
\n" ); document.write( " $\"20%2Ax+=+%284%2Bx%5E2%29%2A3\"$
\n" ); document.write( "or
\n" ); document.write( " $\"20x+=+12+%2B+3x%5E2\"$
\n" ); document.write( "Since this is a quadratic equation, we will get one side equal to zero:
\n" ); document.write( " $\"0+=+3x%5E2+-+20x+%2B+12\"$
\n" ); document.write( "... then factor it (or use the quadratic formula):
\n" ); document.write( " $\"0+=+%283x+-+2%29%28x-6%29\"$
\n" ); document.write( "From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So:
\n" ); document.write( " $\"3x-2+=+0\"$ or $\"x-6+=+0\"$
\n" ); document.write( "Solving these we get:
\n" ); document.write( " $\"3x+=+2\"$ or $\"x+=+6\"$
\n" ); document.write( " $\"x+=+2%2F3\"$ or $\"x+=+6\"$

\n" ); document.write( "Since the problem specifies integers, we must reject x = 2/3. So the only answer to the problem is x=6. \n" ); document.write( "

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