How am I graphing this rational expression wrong on my calculator? So I\'m graph

Question

How am I graphing this rational expression wrong on my calculator?

So I'm graphing the following rational expression in my ti-83 calculator and looking for "error" in my "table" y-value column to confirm removable discontinuties:

x3 -9x/x2-3x

limit as x ?3

When I graph (x3 -9x)/(x2-3x) as typed in my calculator I get the appropriate line with the approriate "error" message in the y-value column at x=0 and x=3 to confirm discontinuities at these x values

When I factor this rational expression to: x(x-3)(x+3)/x(x-3), it's obvious there are discontinuities at x=3 and x=0, but when I type this expression in my calculator to graph as x(x-3)(x+3)/x(x-3) I get a crazy parabolic line without the "error" message at x=3 on "table" to confirm my discontinuities. The graph should be the same as the original expression but how am I typing it wrong?

When I cancel out x to get (x-3)(x+3)/(x-3), the graph looks approriate with the appropriate "error" message in "table" at x=3 (but obviously not at x=0 which is what I want)

When I cancel out x-3 to just get "x+3" the line is also correct

Why isn't my ti-83 appropriately graphing x(x-3)(x+3)/x(x-3) showing the appropriate 'error' message in "table" at x=0 and x=3? How am I typing it wrong?

Explanation / Answer

Hello, there!

Your calculator is just showing the result of what you are providing it an input with, when you type : x(x-3)(x+3)/x(x-3); your calculator follows left to right order in operator precedance, and multiplication and division have the same precedance thus it evaluates it as x(x-3)(x+3)(x-3)/x and hence not showing any error at x=3.

Try typing it as x(x-3)(x+3)/(x(x-3)) as parenthesis () have higher precedance than x and / and hence will give the required output. :)

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