Question

Suppose

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

Answer 1

Answer:

  $((f\circ g)-(g\circ f))(x)=\dfrac{-3x^2-3x-1}{2x^2+x}$

Step-by-step explanation:

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