I need help differentiating [tex] y=\sqrt{x-2}\sqrt{x+1} [/tex](adsbygoogle = window.adsbygoogle || []).push({});

I am using a mix of the chain rule and product rule which my textbook for school wants me to use for this. So suggestions for differant ways of approaching it won't help :P Anyways, thanks in advance for looking over it. It's my first attempt at posting in latex so lets hope it works!

For my work I have:

(dy)/(dx)=[tex](x-2)^{1/2}\frac{d}{dx}(x+1)^{1/2}+(x+1)^{1/2}\frac{d}{dx}(x-2)^{1/2}[/tex]

=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(x+1)^{1/2}(\frac{1}{2})(x-2)^{-1/2}[/tex]

And that is exactly what they have in my textbook, so thats good. But...

For the third part my textbook has

=[tex](\frac{1}{2})(x+1)^{-1/2}(x-2)^{\frac{-1}{2}}(x-2+x+1)[/tex]

This is the step that I am not understanding, it's simple algebra but I am still not quite getting it :( Can someone help?

Then the last step is

=[tex] \frac{2x-1}{2(x+1)^{1/2}(x-2)^{1/2}}[/tex] Which I somewhat understand, but not really.

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PS - For the third step I am getting

=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(\frac{1}{2})(x+1)^{1/2}(x-2)^{-1/2} [/tex]

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# Need help with combination of product and chain rule

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