Add. \[ \frac{2}{x}+\frac{8}{x-4} \] \( \frac{2}{x}+\frac{8}{x-4}=\square \) (Simplify your answer.)

To add the fractions \( \frac{2}{x}+\frac{8}{x-4} \), we first need a common denominator, which would be \( x(x-4) \). Rewriting the fractions, we have: \[ \frac{2(x-4) + 8x}{x(x-4)} \] Now, simplify the numerator: \[ 2(x-4) = 2x - 8 \] Thus, the entire numerator becomes: \[ 2x - 8 + 8x = 10x - 8 \] Now, we can write our combined fraction: \[ \frac{10x - 8}{x(x-4)} \] To simplify further, factor out the common factor in the numerator: \[ 10x - 8 = 2(5x - 4) \] So the expression now looks like this: \[ \frac{2(5x - 4)}{x(x-4)} \] Thus, the simplified answer is: \[ \frac{2(5x - 4)}{x(x-4)} = \underline{\frac{2(5x - 4)}{x(x-4)}} \]