Question

lcm of 6/x-3 - 2/x^2 - 9 = 4/x+3=4/x+3

what do I multiply for the lcm to find the LCD which ones do I multiply

Answer 1

I think your equation is
6/(x−3) − 2/(x^2−9) = 4/(x+3).
Factor x^2 − 9 = (x−3)(x+3), so the LCD (LCM of the denominators) is (x−3)(x+3).

To rewrite each fraction with that LCD:
- 6/(x−3) → multiply top and bottom by (x+3) → 6(x+3)/(x^2−9)
- −2/(x^2−9) → already has the LCD → −2/(x^2−9)
- 4/(x+3) → multiply top and bottom by (x−3) → 4(x−3)/(x^2−9)

Now multiply the whole equation by the LCD (x^2−9) to clear denominators:
6(x+3) − 2 = 4(x−3)

Solve:
6x + 18 − 2 = 4x − 12
6x + 16 = 4x − 12
2x = −28
x = −14

Exclude x = 3 and x = −3 (they make denominators zero). x = −14 is valid.