Question

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Answer 1

\[\frac{2}x+\frac{x}{(x+1)} + \frac{(x+1)}{3x}\]Is that correct?

Answer 2

Factor all of the denominators into their prime factors:

\[x = x\]\[(x+1) = (x+1)\]\[3x= 3*x\]
Multiply all of the unique factors you find together, using the highest power that they appear with:
\[x*(x+1)*3\]
We don't repeat the \(x\) because it only appears as \(x^1\) in either of the denominators that contains it. If one of them had \(x^2\) instead of \(x\), then we would use \(x^2\) instead of \(x\) in the product.

Our least common denominator is \[3x(x+1)\]