It's repetitive and I'm just confused on what to do; I know we have to find a LCD but the fraction-over-fraction-over-fraction is throwing me off.

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

  • $\begingroup$ What's the deal with "$1(x)$"??? Why not just use $x$? $\endgroup$ – barak manos Nov 23 '16 at 5:47
  • $\begingroup$ Whoops, I forgot a couple of parenthesis, I fixed them now. Hopefully it makes sense! $\endgroup$ – Sweetcharge Nov 23 '16 at 5:52

\begin{align} x+\frac{1}{x+\frac{1}{x+\frac{1}{x}}} &= x+\frac{1}{x+\frac{1}{\frac{x^2+1}{x}}}\\&= x+\frac{1}{x+\frac{x}{x^2+1}}\\&= x+\frac{1}{\frac{x^3+2x}{x^2+1}}\\&= x+\frac{x^2+1}{x^3+2x}\\&= \frac{x^4+3x^2+1}{x^3+2x} \end{align}

  • $\begingroup$ Wow, thank you! My work was just messy I guess and I ended up confusing myself. Thank you so much!! $\endgroup$ – Sweetcharge Nov 23 '16 at 6:03
  • $\begingroup$ @Sweetcharge: You're welcome. Feel free to accept the answer by clicking on the V next to it :) $\endgroup$ – barak manos Nov 23 '16 at 6:18

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