Question

Let f (x) =1/ x-1 and g(x) 1-x/xfind and simplify(f-g)(x)

Answer 1

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

Given:

`\begin{gathered} f(x)=(1)/(x-1) \\ g(x)=(1-x)/(x) \end{gathered}`

Find (f-g)(x):

To find what is being asked, we just need to subtract g(x) from f(x):

`\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=(1)/(x-1)-(1-x)/(x) \\ (f-g)(x)=(x-(x-1)(1-x))/(x(x-1)) \\ (f-g)(x)=(x^2-x+1)/(x(x-1)) \end{gathered}`

Therefore:

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