# Thread: Simplyfying fraction with square root

1. ## Simplyfying fraction with square root

Hi guys, I'm new here and I'm trying to solve a question which is probably fairly elementry but I haven't taken math in a while so I'm struggling!

For x < 0, simplify

$\displaystyle \sqrt{x^3+x^2}/x$

I know I'm missing some fundamental step but I just can't get it. Any help would be much appreciated! Thanks.

edit: got help, thanks though!

2. Originally Posted by Regime|Life
Hi guys, I'm new here and I'm trying to solve a question which is probably fairly elementry but I haven't taken math in a while so I'm struggling!

For x < 0, simplify

$\displaystyle \sqrt{x^3+x^2}/x$

I know I'm missing some fundamental step but I just can't get it. Any help would be much appreciated! Thanks.

edit: got help, thanks though!
If you put the denominator INSIDE the square root sign, you have to square it first:

$\displaystyle \frac{\sqrt{x^3+x^2}}{x}$

$\displaystyle = \frac{\sqrt{x^3+x^2}}{\sqrt{x^2}}$

$\displaystyle = \sqrt{\frac{x^3+x^2}{x^2}}$

Not take out a factor of $\displaystyle x^2$ on the top:

$\displaystyle = \sqrt{\frac{x^2(x+1)}{x^2}}$

$\displaystyle = \sqrt{x+1}$

Alternatively, take out the factor of $\displaystyle x^2$ first:

$\displaystyle \frac{\sqrt{x^2(x+1)}}{x}$

$\displaystyle =\frac{\sqrt{x^2}\sqrt{x+1}}{x}$

$\displaystyle =\frac{x\sqrt{x+1}}{x}$

$\displaystyle =\sqrt{x+1}$