2xy + x = 12  Please solve for y. 
Show steps. thank you.

Subtract x from both sides:

2xy + x = 12
    - x      - x
----------------
2xy     = 12 - x

Divide both sides by 2x

   2xy     12 - x
  ----- = --------
    2x       2x

    1
   2xy     12 - x
  ----- = -------
    2x       2x 
     1

           12 - x
      y  = -------
             2x

That's it!  Warning:
Don't do any cancelling
in this stage because the 
numerator contains a 
subtraction!

You can leave the answer
that way. Or else you
can separate it into two
fractions like this
first: 

            12      x
      y  = ---- - ----
            2x     2x
        
And then you can cancel the
2 into the 12 in the first
fraction and cancel the x's
in the second fraction:

             6      1
            12      x
      y  = ---- - ----
            2x     2x 
            1       1

            6     1
      y  = --- - ---
            x     2
 
Either answer is perfectly correct.
They are equivalent even though they
don't look the same.  Use this one

           12 - x
      y  = -------
             2x

if you want y to equal to just one 
fraction. Or use this one

            6     1
      y  = --- - ---
            x     2

if you don't mind having two
separate fractions.  Either way
is correct, just don't try to 
cancel without first separating 
into two fractions.

Edwin