Answer:
no solution
Step-by-step explanation:
x²-4 is (x+2)(x-2), which is your least common multiplier
So first, eliminate the denominators by multiplying all terms by (x+2)(x-2)
(x+2)(x-2)/(x-2) + (6x)(x+2)(x-2)/(x+2)(x-2) = 3(x+2)(x-2)/(x+2)
Then simplify
(x+2) + (6x) = 3(x-2)
combine the variables, and expand the right side of the equation
7x + 2 = 3x - 6
Subtract 2 from both sides
7x = 3x - 8
Substract 3x from both sides
4x = -8
Divide both sides by 4
x = -2
Although x = -2, the final answer is undefined.
Because if you plug x = -2 back into the equation, you would get...
for example, 3/(x+2) will become 3/(-2+2), which is 1/0
it is not possible to divide by 0
anything divided by 0 is undefined, therefore this equation has no solution.
