document.write( "Question 44251: can someone please help me with this problem: 1/3x+6 +2 = 3/x+2 \n" ); document.write( "

Algebra.Com's Answer #29173 by adamchapman(301) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"1%2F%283x%2B6%29+%2B2+=+3%2F%28x%2B2%29\"$
\n" ); document.write( "We want to find out what the value of x is, but this is very hard when x is in a denominator. We can manipulate the expression by multiplyin by (3x+6):
\n" ); document.write( " $\"1+%2B2%283x%2B6%29+=+3%283x%2B6%29%2F%28x%2B2%29\"$
\n" ); document.write( "And then multiplying by (x+2):
\n" ); document.write( " $\"%28x%2B2%29+%2B2%283x%2B6%29%28x%2B2%29+=+3%283x%2B6%29\"$
\n" ); document.write( "Now expand the brackets:
\n" ); document.write( " $\"x%2B2+%2B2%283x%5E2%2B9x%2B12%29+=+9x%2B18%29\"$
\n" ); document.write( " $\"x%2B2%2B6x%5E2%2B27x%2B36=9x%2B18\"$
\n" ); document.write( " $\"6x%5E2%2B28x%2B38=9x%2B18\"$
\n" ); document.write( "Now rearrange so you have zero on the right hand side:
\n" ); document.write( " $\"6x%5E2%2B19x%2B20=0\"$
\n" ); document.write( "Now you can use the quadratic solver $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"$
\n" ); document.write( "where
\n" ); document.write( "a=6
\n" ); document.write( "b=19
\n" ); document.write( "c=20
\n" ); document.write( "And hopefully get the two congutate roots $\"x=-19%2F6-%28sqrt%28199%29i%29%2F6\"$ or $\"x=-19%2F6%2B%28sqrt%28199%29i%29%2F6\"$
\n" ); document.write( "Where \"i\" denotes the imaginary number $\"i=sqrt%28-1%29\"$
\n" ); document.write( "I hope this helps.
\n" ); document.write( "P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
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