document.write( "Question 206612: 1/3x+9 = x+1/x^2+3x + 1/3x^2+9x \n" ); document.write( "

Algebra.Com's Answer #156155 by mickclns(59) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"1%2F3x%2B9+=+x%2B1%2Fx%5E2%2B3x+%2B+1%2F3x%5E2%2B9x\"$ is what you wrote. I think that when you changed your fractions from vertical to horizontal you forgot the parentheses, so I think this is what you meant (correct me if I'm wrong):
\n" ); document.write( " $\"1%2F%283x%2B9%29+=+%28x%2B1%29%2F%28x%5E2%2B3x%29+%2B+1%2F%283x%5E2%2B9x%29\"$ Factor everything you can.
\n" ); document.write( " $\"+1%2F%283%28x%2B3%29%29+=+%28x%2B1%29%2F%28x%28x%2B3%29%29+%2B+1%2F%283x%28x%2B3%29%29+\"$
\n" ); document.write( "Get a (least) common denominator of all the fractions which is 3x(x+3) (why is that the LCD?)
\n" ); document.write( " $\"+x%2F%283x%28x%2B3%29%29+=+3%28x%2B1%29%2F%283x%28x%2B3%29%29+%2B+1%2F%283x%28x%2B3%29%29+\"$ and multiply both sides by the LCD to get rid of fractions.
\n" ); document.write( " $\"x+=+3x%2B3+%2B+1\"$ subtract 3x from both sides and combine like terms
\n" ); document.write( " $\"-2x+=+4\"$
\n" ); document.write( " $\"x+=+-2\"$
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\n" ); document.write( "check answer in ORIGINAL
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?
\n" ); document.write( " $\"1%2F3+=+%28-1%29%2F%284-6%29+%2B+1%2F%2812-18%29\"$ ?
\n" ); document.write( " $\"1%2F3+=+1%2F2+-+1%2F6=%283-1%29%2F6=1%2F3\"$ Yes!
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