N^2+16n+60 over 36-n^2

Factor

36-n^2 is difference of 2 perfect squares

a^2-b^2 = (a-b) (a+b)

6^2-n^2 = (6-n) (6+n)

factor

n^2+16n+60

find what 2 numbers multiply to 60 and add to 16

factors of 60=2,2,3,5

the numbers are 10 and 6

so factored out

(x+6) (x+10)

(x+6) = (6+x)

so the equation is

[ (x+6) (x+10) ]/[ (6+x) (6-x) ]=[ (6+x) / (6+x) ] times (x+10) / ((6-x) = 1 times (x+10) / (6-x)

the answer is (x+10) / (6-x)