Question #N247
The equation $\frac{x^2 - 4}{x-2} = 6$ has one extraneous solution. What is the extraneous solution?
A. -2
B. 2
C. 4
D. 6
Correct Answer is: B
The equation can be simplified by multiplying both sides by $x-2$ to get $x^2 - 4 = 6x - 12$. Rearranging the terms, we get $x^2 - 6x + 8 = 0$. Factoring, we have $(x-2)(x-4)=0$. Therefore, the solutions to the equation are $x=2$ and $x=4$. However, the original expression is undefined when $x=2$, as this would result in division by zero. Therefore, $x=2$ is the extraneous solution.