1. ## Graph?

what does the this look like in a graph. ((x-1)(x+2))/(x(x^2-4))

2. Hello, darcalman!

Graph: . $y \;=\;\frac{(x-1)(x+2)}{x(x^2-4)}$
The function can be reduced . . .

. . $y \;=\;\frac{(x-1)(x+2)}{x(x-2)(x+2)} \;=\;\frac{x-1}{x(x-2)}\quad\hdots$ provided $x \neq -2$

and there is a "hole" in the graph at $\left(-2,-\frac{3}{8}\right)$

With $y \:=\:\frac{x-1}{x(x-2)}$, the x-intercept is (1,0).

There are vertical asymptotes: . $x = 0$ and $x = 2$

As $x$ becomes extremely large, $y$ approaches zero.
. . There is a horizontal asymptote: $y = 0$ (x-axis).

Test various values of $x$ and determine when the graph is above or below the x-axis.

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