1. Find Function g

Given f(x) = 1/x and (f/g) (x) = (x + 1)/( x^2 - x), find the function g.

2. Originally Posted by blueridge
Given f(x) = 1/x and (f/g) (x) = (x + 1)/( x^2 - x), find the function g.
I assume that $\displaystyle (f/g)(x) = \frac{f(x)}{g(x)} = \frac{1}{xg(x)} = \frac{x+1}{x^2-x}$

Rewrite,
$\displaystyle \frac{1}{xg(x)} = \frac{x+1}{x(x-1)}$
Take reciprocals,
$\displaystyle xg(x) = \frac{x(x-1)}{x+1}$
Thus,
$\displaystyle g(x) = \frac{x-1}{x+1}$

3. ok

You said "thus" but did not complete your statement.

4. Originally Posted by blueridge
You said "thus" but did not complete your statement.
Notice the LHS has $\displaystyle x$ as a product and the RHS has $\displaystyle x$ as a product. Thus, I divided the x's from the two sides. And was let with $\displaystyle g(x)$ what I was looking for.