Add. \[ \frac{x}{x-2}+\frac{3}{4 x-8} \]

To add the fractions, we first need a common denominator. Notice that \( 4x - 8 \) can be factored as \( 4(x - 2) \). Thus, the least common denominator (LCD) is \( 4(x - 2) \). Rewriting each fraction with the common denominator gives us: 1. For \(\frac{x}{x-2}\), we multiply the numerator and denominator by 4: \[ \frac{x \cdot 4}{(x - 2) \cdot 4} = \frac{4x}{4(x - 2)} \] 2. The second fraction is already expressed with the common denominator: \[ \frac{3}{4(x - 2)} \] Now we can combine the two fractions: \[ \frac{4x + 3}{4(x - 2)} \] Thus, the final result is: \[ \frac{4x + 3}{4(x - 2)} \]