SOLUTION: can someone please help me with this problem: 1/3x+6 +2 = 3/x+2

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Question 44251: can someone please help me with this problem: 1/3x+6 +2 = 3/x+2
Found 2 solutions by adamchapman, MathTherapy:
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%283x%2B6%29+%2B2+=+3%2F%28x%2B2%29
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):
1+%2B2%283x%2B6%29+=+3%283x%2B6%29%2F%28x%2B2%29
And then multiplying by (x+2):
%28x%2B2%29+%2B2%283x%2B6%29%28x%2B2%29+=+3%283x%2B6%29
Now expand the brackets:
x%2B2+%2B2%283x%5E2%2B9x%2B12%29+=+9x%2B18%29
x%2B2%2B6x%5E2%2B27x%2B36=9x%2B18
6x%5E2%2B28x%2B38=9x%2B18
Now rearrange so you have zero on the right hand side:
6x%5E2%2B19x%2B20=0
Now you can use the quadratic solver x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+
where
a=6
b=19
c=20
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
Where "i" denotes the imaginary number i=sqrt%28-1%29
I hope this helps.
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

Answer by MathTherapy(10703) About Me  (Show Source):
You can put this solution on YOUR website!
can someone please help me with this problem:  1/3x+6 +2 = 3/x+2

The answer provided by the other person who responded, is WRONG!!

Based on the person's statement, if he/she wants to do well in the tutoring business, the person needs
to know how to check his/her work, before submitting it. And, after doing so, this person also needs to
CHECK whatever answer he/she has derived. 

     1%2F%283x+%2B+6%29+%2B+2+=+3%2F%28x+%2B+2%29
    1%2F3%28x+%2B+2%29+%2B+2+=+3%2F%28x+%2B+2%29
1 + 2(3)(x + 2) = 3(3) --- Multiplying by LCD, 3(x + 2)
    1 + 6x + 12 = 9
        6x = 9 - 13
        6x = - 4 
        highlight%28x%29+=+%28-+4%29%2F6+=+highlight%28%28-+2%29%2F3%29

If you DON’T use an LCD, but a COMMON DENOMINATOR instead, you could end up with a quadratic equation
that can be FACTORIZED nicely, and result in another solution, - 2. However, this solution is an
EXTRANEOUS one, as it leads to both original fractional-expressions, being UNDEFINED!