Add: \( \frac{2}{x+2}+\frac{-4}{x+5} \)

To combine the fractions \( \frac{2}{x+2}+\frac{-4}{x+5} \), you first find a common denominator, which will be \( (x+2)(x+5) \). The first fraction becomes \( \frac{2(x+5)}{(x+2)(x+5)} \), and the second fraction transforms to \( \frac{-4(x+2)}{(x+2)(x+5)} \). Now, combine the numerators: \[ \frac{2(x+5) - 4(x+2)}{(x+2)(x+5)} \] Simplify the numerator: \[ 2x + 10 - 4x - 8 = -2x + 2 \] Thus, the combined expression is: \[ \frac{-2x + 2}{(x+2)(x+5)} \quad \text{or you can write it as} \quad \frac{2(1-x)}{(x+2)(x+5)} \] And there you have it!