Rationalize the numerator: (3/sqrt[x] - 3/sqrt[x+h]) / h

[loljujlol]

Please help me rationalize the numerator of:

\(\displaystyle \dfrac{ \left( \dfrac{3}{\sqrt{x\,}}\, -\, \dfrac{3}{\sqrt{x\, +\, h\,}} \right) } {h}\)

The back of the book answer is:

\(\displaystyle \dfrac{3}{\left( \sqrt{x\,} \cdot (x\, +\, h)\, +\, x \cdot \sqrt{x\, +\, h\,} \right)}\)

I have tried but cannot seem to get the answer. I believe I am having a simplifying problem, but if anyone can show me steps, that would be highly appriciated.

 

[stapel]

Please help me rationalize the numerator of:

\(\displaystyle \dfrac{ \left( \dfrac{3}{\sqrt{x\,}}\, -\, \dfrac{3}{\sqrt{x\, +\, h\,}} \right) } {h}\)

The back of the book answer is:

\(\displaystyle \dfrac{3}{\left( \sqrt{x\,} \cdot (x\, +\, h)\, +\, x \cdot \sqrt{x\, +\, h\,} \right)}\)

I have tried...

Great! Please reply showing what you have done, so we can help you find any errors and get back going again. Thank you!