# How do you rationalize the denominator and simplify 4/ (sqrt x +1)?

I found: (4(sqrt(x)-1))/((x-1)
You can multiply and divide by $\sqrt{x} - 1$:
$\frac{4}{\sqrt{x} + 1} \cdot \frac{\sqrt{x} - 1}{\sqrt{x} - 1} =$
$= \frac{4 \left(\sqrt{x} - 1\right)}{{\left(\sqrt{x}\right)}^{2} \cancel{- \sqrt{x}} + \cancel{\sqrt{x}} - 1}$
=(4(sqrt(x)-1))/((x-1)