# How do you simplify (x^2n-1)/( x^n-3)?

Jun 1, 2015

I will assume that the expression in the question should be formatted as:

$\frac{{x}^{2 n} - 1}{{x}^{n} - 3}$

$= \frac{{\left({x}^{n}\right)}^{2} - {1}^{2}}{{x}^{n} - 3}$

$= \frac{\left({x}^{n} - 1\right) \left({x}^{n} + 1\right)}{{x}^{n} - 3}$

$= \frac{\left({x}^{n} - 3\right) \left({x}^{n} + 1\right) + 2 \left({x}^{n} + 1\right)}{{x}^{n} - 3}$

$= {x}^{n} + 1 + \frac{2 \left({x}^{n} + 1\right)}{{x}^{n} - 3}$

$= {x}^{n} + 1 + \frac{2 \left({x}^{n} - 3\right) + 8}{{x}^{n} - 3}$

$= {x}^{n} + 3 + \frac{8}{{x}^{n} - 3}$

With the restriction ${x}^{n} \ne 3$