Question 1151162
<pre>
She's right.  I just guessed and added the words "is a positive integer" so your
sentence would make sense. I also put parentheses around (x^3-6x^2+3x+10) so
that the whole thing would be the denominator and not just the first term x^3 by
the PEMDAS rule.

{{{18(x^2-7x+10)/(x^3-6x^2+3x+10)}}}

Factoring, using synthetic division to factor the denominator,

{{{18(x-5)(x-2)/((x+1)(x-2)(x-5))}}}

Canceling the (x-5)'s and the (x-2)'s

{{{18/(x+1)}}} must be a positive integer.

x+1 must be a factor of 18.  The factors of 18 are 1,2,3,6,9,18.

x+1 = 1,2,3,6,9,18
  x = 0,1,2,5,8,17

Adding: 0+1+2+5+8+17 = 33 

That's the answer if I happen to have guessed the right words to add to make
what you wrote make sense.

Edwin</pre>