document.write( "Question 1063043: the denominator of a fraction exceeds the numerator by 2. If the numerator is decreased by 1 and the denominator is increased by 3,the value of the resulting fraction is 1/2 find the original fraction? with linear equation \n" ); document.write( "

Algebra.Com's Answer #678069 by Fombitz(32388) $\"\"$ $\"About$

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Original fraction,
\n" ); document.write( " $\"X%2F%28X%2B2%29\"$
\n" ); document.write( "New fraction,
\n" ); document.write( " $\"%28X-1%29%2F%28X%2B2%2B3%29=%28X-1%29%2F%28X%2B5%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"%28X-1%29%2F%28X%2B5%29=%281%2F2%29%28X%2F%28X%2B2%29%29\"$
\n" ); document.write( " $\"2%28X-1%29%28X%2B2%29=X%28X%2B5%29\"$
\n" ); document.write( " $\"2%28X%5E2%2B2X-X-2%29=X%5E2%2B5X\"$
\n" ); document.write( " $\"2X%5E2%2B2X-4=X%5E2%2B5X\"$
\n" ); document.write( " $\"X%5E2-3X-4=0\"$
\n" ); document.write( " $\"%28X-4%29%28X%2B1%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"X-4=0\"$
\n" ); document.write( " $\"X=4\"$
\n" ); document.write( "and
\n" ); document.write( " $\"X%2B1=0\"$
\n" ); document.write( " $\"X=-1\"$
\n" ); document.write( "So the original fraction was
\n" ); document.write( " $\"4%2F%284%2B2%29=4%2F6=2%2F3\"$
\n" ); document.write( "or
\n" ); document.write( " $\"-1%2F%28-1%2B2%29=-1%2F1=-1\"$
\n" ); document.write( " \n" ); document.write( "

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