find the horizontal asymptote of the function h(x)=(-x^2 + 5x - 2)/(x^2 + x). y=

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator $-x^{2}+5x - 2$ is $n = 2$, and the degree of the denominator $x^{2}+x$ is $m=2$.

Step2: Find the horizontal - asymptote

When $n = m$, the horizontal asymptote $y$ is the ratio of the leading - coefficients. The leading coefficient of the numerator is $a=-1$ and the leading coefficient of the denominator is $b = 1$. So, $y=\frac{a}{b}=\frac{-1}{1}=-1$.

Answer:

$y=-1$