Question

Hello, I’m struggling with this problem. What is the answer?

Answer 1

Okay, here we have this:

$\frac{\sqrt[]{x+3}-\sqrt[]{x}}{3}$

And we need to rationalize the numerator, so let's do it:

$\frac{\sqrt[]{x+3}-\sqrt[]{x}}{3}\cdot\frac{\sqrt[]{x+3}+\sqrt[]{x}}{\sqrt[]{x+3}+\sqrt[]{x}}$

Now let's simplify:

$\frac{x+3-x}{3(\sqrt[]{x+3}+\sqrt[]{x})}=\frac{3}{3(\sqrt[]{x+3}+\sqrt[]{x})}$

$=\frac{1}{\sqrt[]{x+3}+\sqrt[]{x}}$