Simplifying the product (x^(n+1)/√(n+1))·(√n/x^n)

[tony873004]

Homework Statement

My notes are missing a step. How do I get $$\frac{{x^{n + 1} }}{{\sqrt {n + 1} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x\sqrt n }}{{\sqrt {n + 1} }}$$

Homework Equations

I'm trying like this, but I don't seem to be arriving at the same step as the example:
$$\frac{{x^{n + 1} }}{{\sqrt {n + 1} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt {n\left( {1 + \frac{1}{n}} \right)} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt n \sqrt {\left( {1 + \frac{1}{n}} \right)} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt {\left( {1 + \frac{1}{n}} \right)} }}\frac{1}{{x^n }}$$

Thanks!

 

[tony873004]

Never mind. I figured it out. x^(n+1)/x^n = x