SOLUTION: 1/3x+9 = x+1/x^2+3x + 1/3x^2+9x

Algebra ->  Equations -> SOLUTION: 1/3x+9 = x+1/x^2+3x + 1/3x^2+9x      Log On


   

Question 206612: 1/3x+9 = x+1/x^2+3x + 1/3x^2+9x
Answer by mickclns(59) About Me  (Show Source):
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):
1%2F%283x%2B9%29+=+%28x%2B1%29%2F%28x%5E2%2B3x%29+%2B+1%2F%283x%5E2%2B9x%29 Factor everything you can.
+1%2F%283%28x%2B3%29%29+=+%28x%2B1%29%2F%28x%28x%2B3%29%29+%2B+1%2F%283x%28x%2B3%29%29+
Get a (least) common denominator of all the fractions which is 3x(x+3) (why is that the LCD?)
+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.
x+=+3x%2B3+%2B+1 subtract 3x from both sides and combine like terms
-2x+=+4
x+=+-2
 
check answer in ORIGINAL
?
1%2F3+=+%28-1%29%2F%284-6%29+%2B+1%2F%2812-18%29 ?
1%2F3+=+1%2F2+-+1%2F6=%283-1%29%2F6=1%2F3 Yes!