h(x) = (x² - 3x)/x\nlim h(x)\nx→0

Explanation:

Step1: Simplify the function

First, simplify $h(x)=\frac{x^{2}-3x}{x}$. Factor out $x$ from the numerator: $h(x)=\frac{x(x - 3)}{x}$. Since $x\neq0$ when taking the limit, we can cancel out the $x$ terms, so $h(x)=x - 3$ for $x\neq0$.

Step2: Calculate the limit

Now, find $\lim_{x\rightarrow0}h(x)$. Substitute $x = 0$ into the simplified - function $y=x - 3$. Using the direct - substitution property of limits for polynomial functions, we have $\lim_{x\rightarrow0}(x - 3)=0-3=-3$.

Answer:

$-3$