Question 815092
Are you asking for a simplification of {{{F(x)=(x^2+7x+10)/(x^2-7x-18)}}} ?


Factorize the numerator and denominator.  Look for common factors which are equivalent to a factor of 1.  Just be aware than if you cancel these, the meaning of the simplified form will be changed.


Numerator:  (x+2)(x+5)
Denominator:  (x+2)(x-9)


The function can be rewritten, {{{F(x)=((x+2)(x+5))/((x+2)(x-9))}}}.
BEFORE simplification, you must understand that the function has a skipped point at {{{x=-2}}} and an asymptote at {{{x=9}}}.


The simplification is to cancel the apparant {{{(x+2)/(x+2)}}} as a factor of 1:
{{{highlight(h(x)=(x+5)/(x-9))}}}.
You will note that I changed the name of this function.  The discontinuity at {{{x=-2}}} is now gone, so the h(x) IS continuous there, but the asymptote at {{{x=9}}} remains for h(x) as it does for F(x).