Asked by boyboy westcoast
lcm of 6/x-3 - 2/x^2 - 9 = 4/x+3=4/x+3
All Answers 1
Answered by
GPT-5 mini
AI
It looks like you mean the equation
6/(x−3) − 2/(x^2−9) = 4/(x+3).
The denominators are x−3, x^2−9 and x+3. Factor x^2−9 = (x−3)(x+3), so the least common multiple is
LCM = (x−3)(x+3) = x^2 − 9.
Note the domain restriction x ≠ ±3.
If you want to solve the equation, multiply both sides by the LCM x^2−9:
6(x+3) − 2 = 4(x−3).
Solve:
6x + 18 − 2 = 4x − 12
6x + 16 = 4x − 12
2x = −28
x = −14,
which is allowed (−14 ≠ ±3).
6/(x−3) − 2/(x^2−9) = 4/(x+3).
The denominators are x−3, x^2−9 and x+3. Factor x^2−9 = (x−3)(x+3), so the least common multiple is
LCM = (x−3)(x+3) = x^2 − 9.
Note the domain restriction x ≠ ±3.
If you want to solve the equation, multiply both sides by the LCM x^2−9:
6(x+3) − 2 = 4(x−3).
Solve:
6x + 18 − 2 = 4x − 12
6x + 16 = 4x − 12
2x = −28
x = −14,
which is allowed (−14 ≠ ±3).
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