Find (f ∘ g)(x) when f(x) = x/x-1 and g(x) = -3/x

Question

(f ∘ g)(x) = 

(f ∘ g)(x) = 

(f ∘ g)(x) = 

(f ∘ g)(x) = 

(f ∘ g)(x) = 

Answer 1

f(x) = x/(x - 1)

g(x) = -3/x

(f _° g)(x) = f(g(x))

= f(-3/x)

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

= (-3/x) / [(-3/x) - (x/x)]

= (-3/x) / [(-3 - x)/x]

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

= (3/x) / [(x + 3)/x]

= (3/x)*[x/(x + 3)] = 3/(x + 3)