Is the LCD of x/2x-4 and 5x/12x-24 not 24(x-2)? The original question is x/2x-4 + 5x/12x-24 and I factored the denominators first so that I could find the LCD. And I got:

x/2(x-2) + 5x/12(x-2)

After that, I multiplied up to the LCD and got:

x/2(x-2) + 5x/12(x-2)
= x/2(x-2)*(12/12) + 5x/12(x-2)*(2/2)
= 12x/24(x-2) + 10x/24(x-2)
= 22x/24(x-2)

What did I do wrong?

2 answers

2x-4 = 2(x-2)
12x-24 = 12(x-2)

So, the LCD is 12(x-2), not 24(x-2)

(6x+5x) / 12(x-2)
11x/12(x-2)

This is the same as your answer, if you cancel a factor of 2 which you did not need in the LCD.
I don't think I exactly understand how to figure out the LCD. So how do you know that the LCD is 12(x-2) not 24(x-2)?