Question

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

Answer 1

Answer:

$(f-g)(x)=\frac{x^{2}-x+1}{x(x-1)}$

Given:

$\begin{gathered} f(x)=\frac{1}{x-1} \\ g(x)=\frac{1-x}{x} \end{gathered}$

Find (f-g)(x):

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

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

Therefore:

$(f-g)(x)=\frac{x^{2}-x+1}{x(x-1)}$