Add. 29. \( \frac{4 x}{x+4}+\frac{6}{x+2} \)

To add the fractions \( \frac{4 x}{x+4}+\frac{6}{x+2} \), we first need a common denominator. The least common denominator (LCD) for \( x + 4 \) and \( x + 2 \) is \( (x + 4)(x + 2) \). Rewriting each fraction: - The first fraction becomes \( \frac{4x(x+2)}{(x+4)(x+2)} \). - The second fraction becomes \( \frac{6(x+4)}{(x+4)(x+2)} \). Now, combine them over the common denominator: \[ \frac{4x(x+2) + 6(x+4)}{(x+4)(x+2)}. \] Expanding the numerators: \[ 4x^2 + 8x + 6x + 24 = 4x^2 + 14x + 24. \] So, the final expression becomes: \[ \frac{4x^2 + 14x + 24}{(x+4)(x+2)}. \] And this is your final answer!