Find Function g

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

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

Let me see.

I know that f(x) = 1/x. I also know that (f/g)(x) = f(x)/g(x).

Here's my set up:

(1/x) ÷ (x + 1)(x^2 - x). . .This is a complex fraction that can be simplified.

(1/x) ÷ (x + 1)/(x^2 - x) becomes (1/x) • (x^2 - x)/(x + 1).

When I continue to simplify, I get the following:

x(x - 1)/x(x + 1), which finally simplifies to (x - 1)/(x + 1).

You say?

[Eigenvalue]

Yes, this is correct