Final answer:
To solve the given rational equation, we simplify the expression, multiply by the conjugate, and solve for x. The equation has no solution.
Step-by-step explanation:
To solve the rational equation 12/(2-2√3) = 1, we need to isolate the variable x. First, let's simplify the expression on the left side. We can do this by multiplying the numerator and denominator by the conjugate of the denominator, which is 2+2√3. This gives us:
12/(2-2√3) * (2+2√3)/(2+2√3) = 1
Simplifying further, we get:
(24+24√3)/(4-12) = 1
Now, distribute and combine like terms:
24+24√3 = -8
Finally, solve for x:
24√3 = -32
√3 = (-32)/24
√3 = -4/3
This is not possible since the square root of 3 is a positive number. Therefore, the equation has no solution. Hence, the correct answer is option C. There is no solution.
Learn more about Solving rational equations