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?

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  1. 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)

    This is the same as your answer, if you cancel a factor of 2 which you did not need in the LCD.

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    posted by Steve
  2. 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)?

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    posted by Emily J

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