Answer
$$\frac{2x^2-20}{\left(x+2\right)\left(x-5\right)\left(x-4\right)}$$
Work Step by Step
Creating like denominators in order to combine the fractions, we obtain:
$$\frac{x+4}{\left(x+2\right)\left(x-5\right)}+\frac{x-2}{\left(x-4\right)\left(x-5\right)}\\ \frac{\left(x+4\right)\left(x-4\right)}{\left(x+2\right)\left(x-5\right)\left(x-4\right)}+\frac{\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x-5\right)\left(x+2\right)} \\ \frac{\left(x+4\right)\left(x-4\right)+\left(x-2\right)\left(x+2\right)}{\left(x+2\right)\left(x-5\right)\left(x-4\right)} \\ \frac{2x^2-20}{\left(x+2\right)\left(x-5\right)\left(x-4\right)}$$
