Question

Suppose

f(x)= x/(x+1) and g(x)= (x+1)/x. Then ((f∘g)−(g∘f))(x)=

Answer 1

`((f\circ g)-(g\circ f))(x)=(-3x^2-3x-1)/(2x^2+x)`

Explanation:

`((f\circ g)-(g\circ f))(x)=((x+1)/(x))/((x+1)/(x)+1)-((x)/(x+1)+1)/((x)/(x+1))\\\\=(x+1)/(2x+1)-(2x+1)/(x)=(x(x+1)-(2x+1)^2)/(x(2x+1))\\\\=\bf{(-3x^2-3x-1)/(2x^2+x)}`