x/(x-2) - (x-6)/(x-4)
if u have
x/(x-2) - (x-6)/(x-4) = 0
then multiply by x-4 and x-2 to get
x(x-4) - (x-6)(x-2)
the multiply out the brackets
x^2 - 4x - x^2 + 8x - 12 = 0
then collect like terms to get
4x - 12 = 0,
so x = 3
x/(x-2) - (x-6)/(x-4)
GCM- greatest common denominator
Or is it LCD - least common denominator? I think GCM.
either way, get a common, meaning equal, denominator (bottom part of each fraction) for both fractions.
So,
$\displaystyle \frac {x*(x-4)}{(x-2)*(x-4)}-\frac {(x-6)*(x-2)}{(x-4)*(x-2)}$
Make it all one fraction, now that we have a common denominator.
Subtract the numerator, the tops, if possible to get rid of terms.
ex. (x-2)- (x-2) and cancel (not saying exists above, its just an example)
There you go.
It's LCD. Lowest Common Denominator. But "lowest" isn't all that important here because all you do is multiply that two denominators together.
So from the post above:
The (x-4) and (x-2) cancel out leaving you with:
x-x-6 / x-2-x-4
which simplifies to:
-6/-6 which is 1.
I hope I'm right. I would double check. :P