simplify 10-x^2-3x/x^2+2x-8 identify any x-values for which the expression is undefined. I got the answer (-x-5)/(x+4) but what about the undefined values? Is it just -4 or -4 and 2?

Question

mathmale · Answer

It's not about an "undefined value," but rather about "an x-value at which the function is undefined."

I see your denominator is x^2+2x-8.  Factor this.  Set each factor = to 0, separately.  Each of those two "solutions" is "a value at which the given function is undefined."  Try it.

anonymous · Answer

I did, and I got (-x+2)(x+5)/(x-2)(x+4)
After that I took out a -1 from (-x+2) so It'd become -1(x+5)/(x+4)
The final answer turns our to be -x-5/x+4 
I'm still a bit confused about the whole undefined matter though....

mathmale · Answer

A rational function (not an x-value) becomes undefined if its denominator becomes zero.
Your denominator here is (x-2)(x+4), so your function becomes undef. at either x=2 or x=-4.

mathmale · Answer

$$\frac{ 10-x^2-3x }{ x^2+2x-8 }=\frac{ -(x-2)(x-5) }{ (x-2)(x-4) }$$

mathmale · Answer

and you are allowed to cancel the two (x-2) factors.  However, even after you've cancelled them, you can NOT let x = 2, because the original function would be undefined at x=2.  Note that the original function is also undefined at x=4.

anonymous · Answer

OHHH that makes so much sense! Thank you so much :D

mathmale · Answer

My great pleasure!