Which of the following would be an extraneous solution to the following equation if it's a solution? \( \frac{x+8}{x-2}+\frac{6}{x}=\frac{x-4}{x} \) -8 4 6 2
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To start, let’s solve the equation \( \frac{x+8}{x-2}+\frac{6}{x}=\frac{x-4}{x} \). When solving rational equations, it’s crucial to look out for values that make denominators zero, as those are not valid solutions. In this case, \( x \) cannot be 2 or 0, since they will lead to division by zero. Now, checking the provided options: plugging in 2 will cause the denominator in the first term to break down, which means 2 is an extraneous solution! Always check the potential solutions against the original equation to catch any sneaky false leads!