In the following problem, what are the domain restrictions? **i worked out the answer but I'm not sure if 5 would be a restriction or not since it was in the denominator in some steps of the problem**

Question

owlstudies · Answer

$$\frac{ 2\frac{ x+3 }{ x-5 }+7 }{ \frac{ x+3 }{ x-5 }-6 }$$

owlstudies · Answer

I simplified it to : $$\frac{ 9x-29 }{ -5x+33 }$$

owlstudies · Answer

One of the domain restrictions is 33/5, but would the other one be 5, or no?

mathmate · Answer

Yes, 5 is also a restriction, because it occurs in the denominator of the numerator (sounds confusing, but you understand what I mean).
If there were no restriction, one would be dividing a zero by a zero.

owlstudies · Answer

okay thank you!

mathmate · Answer

You're welcome!  :)