Answer
$$-\frac{x^2+4}{x+2}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{\left(x-1\right)}{x+2}\times \frac{4+x^2}{\left(1-x\right)}\\ \frac{\left(x-1\right)\left(4+x^2\right)}{\left(x+2\right)\left(x-1\right)}\\ -\frac{x^2+4}{x+2}$$