How to find the excluded values of this rational expression?

Question

calculusxy · Answer

$$\large \frac{x+8}{27x^3 - 9x^2} - 3$$

calculusxy · Answer

@jim_thompson5910

satellite73 · Answer

set the denominator equal to zero, solve for $x$

satellite73 · Answer

i.e. solve $$27x^3-9x^2=0$$which factors easily

calculusxy · Answer

So I actually factored the denominator and got $9x^2(3x - 1)$.

calculusxy · Answer

@satellite73

satellite73 · Answer

yes

satellite73 · Answer

now set each factor equal to zero and solve for $x$

satellite73 · Answer

not much to solve for the first one

mathmale · Answer

The point is:  x cannot take on any value that makes the denominator = to 0.  So, play the devil's advocate and set the den. = to 0; solve for x.  Those are the excluded values.

calculusxy · Answer

So would the excluded values be 0 and $\frac{1}{3}$?

satellite73 · Answer

yes

calculusxy · Answer

But my teacher said that the excluded values should be the ones that can be used on both of the fractions.

calculusxy · Answer

I was confused with that because both of the excluded values don't work on both of them.

mathmale · Answer

Explain further.  You have only one fraction here.  Using the denom. of the first fraction to make the 2nd term into a fraction will not change the excluded values.

mathmale · Answer

Your only worry is whether your 2 excluded values make the ONE denominator = 0.  If yes, then you have found the excluded values.  That -3 will not be affected by "x" in the denom. of the rational fraction.

calculusxy · Answer

I don't understand what you mean by `"Your only worry is whether your 2 excluded values make the ONE denominator = 0."`.

matlee · Answer

idk what i did or if this is right but i was on it so i put it in. http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=7db1532e6b11e55451ceb6caf72d6a2b&title=Rational%20Expressions%20Calculator&theme=blue&i0=

mathmale · Answer

calculusxy:  At this point, what do you still need to learn / do?  If you're focusing ONLY on excluded values, you could forget about that     -3     term entirely.

You have found 2 values:   0 and 1/3 .   substitute these into the rational fraction.  Does the denominator go to zero in both cases (tested separately)?