I'm trying to compose [tex]f(x)= x + \frac{1}{x}[/tex] with itself. e.g. [tex]f \circle f[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I have [tex] x + \frac{1}{x} + \frac{1}{x+(1/x)} [/tex]

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

[tex] x + \frac{1}{x} + \frac{x}{x^2+1} [/tex]

This is not the correct answer according to the book.

Books is:

[tex] \frac{x^4+3x^2+1}{x(x^2+1)} [/tex]

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

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# Homework Help: Problem composing a rational function with itself.

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