document.write( "Question 758532: The numerator of a certain fraction is 4 times the denominator. If 6 is added to both the numerator and denominator, the resulting fraction is equivalent to 2. What was the original fraction? \n" ); document.write( "

Algebra.Com's Answer #461553 by MathLover1(20850) $\"\"$ $\"About$

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Let $\"x\"$ be the denominator.
\n" ); document.write( "Then, the numerator is $\"4x\"$ , and the fraction is $\"4x%2Fx\"$ , which is equivalent to $\"4\"$ .
\n" ); document.write( " $\"4x%2Fx=2\"$
\n" ); document.write( "If you add $\"6\"$ to both the numerator and the denominator, the resulting fraction is
\n" ); document.write( " $\"%284x%2B6%29%2F%28x%2B6%29=2\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiplying both sides of the equal sign times $\"%28x%2B6%29\"$ we get
\n" ); document.write( " $\"%28%284x%2B6%29%2F%28x%2B6%29%29%2A%28x%2B6%29=2%2A%28x%2B6%29\"$
\n" ); document.write( " $\"4x%2B6=2%28x%2B6%29\"$
\n" ); document.write( " $\"4x%2B6=2x%2B12\"$
\n" ); document.write( " $\"4x-2x=12-6\"$
\n" ); document.write( " $\"2x=6\"$
\n" ); document.write( " $\"x=3\"$ .......denominator
\n" ); document.write( " $\"4x=4%2A3=12\"$ ......numerator\r
\n" ); document.write( "\n" ); document.write( "so, fraction is $\"12%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( "if $\"6\"$ is added to both the numerator and denominator, we have\r
\n" ); document.write( "\n" ); document.write( " $\"%2812%2B6%29%2F%283%2B6%29=18%2F8=2\"$ \r
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