Question 156272
Note that:
{{{81 - x^2=-(x^2-81)}}}
So
{{{x/(x^2-81)+9/(81-x^2)}}}
={{{x/(x^2-81)+9/(-(x^2-81))}}}
={{{x/(x^2-81)-9/(x^2-81)}}}
={{{(x-9)/(x^2-81)}}}
={{{(x-9)/(x^2-9^2)}}}
={{{(x-9)/((x+9)(x-9))}}}  (factor x^2-9^2 into (x+9)(x-9))
={{{cross((x-9))/((x+9)cross((x-9)))}}}
={{{1/(x+9)}}}