Problem composing a rational function with itself.

[fedaykin]

I'm trying to compose $$f(x)= x + \frac{1}{x}$$ with itself. e.g. $$f \circle f$$

I have $$x + \frac{1}{x} + \frac{1}{x+(1/x)}$$

Now I multiplied $$\frac{1}{x + (1/x)} * \frac{x}{x}$$ and I got:

$$x + \frac{1}{x} + \frac{x}{x^2+1}$$

This is not the correct answer according to the book.
Books is:

$$\frac{x^4+3x^2+1}{x(x^2+1)}$$

I have no idea how they got that. I can't get a common denominator and get that.

 

[Dick]

Try a forward slash on the final $$. But your answer is also correct. Put everything over a common denominator of x*(x^2+1).$$

 

[fedaykin]

Thank you very very very much. My first 100 in calc so far awaits me tomorrow!

 

[Dick]

Good luck!