Rmember (a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)this is just alot of busy work
find f+g first then find f-g
f+g=(x-4)/(x+9)+(x-9)/(x+4)
make denomenator the same
multiply left one by (x+4)/(x+4) and right one by (x+9)/(x+9)
[(x-4)(x+4)]/[(x+9)(x+4)]+[(x-9)(x+9)]/[(x+9)(x+4)]
[x²-16]/[(x+9)(x+4)]+[x²-81]/[(x+9)(x+4)]
[x²+x²-16-81]/[(x+9)(x+4)]
[2x²-97]/[(x+9)(x+4)]
now f-g
[x²-16]/[(x+9)(x+4)]-[x²-81]/[(x+9)(x+4)]
[x²-x²-16+81]/[(x+9)(x+4)]
[65]/[(x+9)(x+4)]
now we got
invert and multiply
2nd option
find f+g first then find f-g
f+g=(x-4)/(x+9)+(x-9)/(x+4)
make denomenator the same
multiply left one by (x+4)/(x+4) and right one by (x+9)/(x+9)
[(x-4)(x+4)]/[(x+9)(x+4)]+[(x-9)(x+9)]/[(x+9)(x+4)]
[x²-16]/[(x+9)(x+4)]+[x²-81]/[(x+9)(x+4)]
[x²+x²-16-81]/[(x+9)(x+4)]
[2x²-97]/[(x+9)(x+4)]
now f-g
[x²-16]/[(x+9)(x+4)]-[x²-81]/[(x+9)(x+4)]
[x²-x²-16+81]/[(x+9)(x+4)]
[65]/[(x+9)(x+4)]
now we got
invert and multiply
2nd option