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

Hello, I’m struggling with this problem. What is the answer?-example-1
User Bahaa Hany
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1 Answer

17 votes
17 votes

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}}

User TheTiger
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