Algebra 2 Find (f+g)(x)

Question

Answer 1

put f and g with common denominators then add their numerators

LCD = (x+3)(x-3)(x+6)

then numerators are x^5(x+6) and x^4(x+3)

so (f+g)(x) = (x^6 +7x^5 + 3x^4)/(x^3 +6x^2 -9y -54)

= x^4(x^2 +7x +3)/(x-3)(x+3)(x+6) in factored form