Let f(x)--and g(x)- Find and simplify (fog)(x)

Question

Let f(x)=(x/(x-3))--and g(x)=1/(x+2) Find and simplify (fog)(x)

Answer 1

Let f(x)=(x/(x-3)) and g(x)=1/(x+2)

Calculate the (fog)(x).

(fog)(x) =f(g(x))

            =f(1/(x+2))

            =[(1/(x+2)]/[((1/(x+2))-3)]

            =[(1/(x+2)]/[(1-3(x+2)/(x+2))]

            =1/(1-3x-6)

            =1/(-3x-5)