How do you simplify (x^(2n) xx x^(3n-1)) / x^(n+2)  leaving only positive exponents?

Apr 13, 2016

${x}^{4 n - 3}$

Explanation:

Consider just the exponents:

Write as: $2 n + \left(3 n - 1\right) - \left(n + 2\right)$

$2 n + 3 n - 1 - n - 2$

$4 n - 3$

So we have: ${x}^{4 n - 3}$

This is positive for $n > \frac{3}{4}$

As $n$ is a counting number it is not likely to have $n < 1$