anonymous
  • anonymous
Help please
Calculus1
katieb
  • katieb
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anonymous
  • anonymous
|dw:1441001669103:dw|
anonymous
  • anonymous
simplifying radical expressions
jim_thompson5910
  • jim_thompson5910
does it want you to apply a limit? or just simplify?

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anonymous
  • anonymous
just simplify
jim_thompson5910
  • jim_thompson5910
ok like before, multiply top and bottom by \(\Large \sqrt{x+h}+\sqrt{x}\) \[\Large \frac{\sqrt{x+h}-\sqrt{x}}{h}\] \[\Large \frac{(\sqrt{x+h}-\sqrt{x})}{h}\times \color{red}{\frac{(\sqrt{x+h}+\sqrt{x})}{(\sqrt{x+h}+\sqrt{x})}}\]
jim_thompson5910
  • jim_thompson5910
tell me what you get in the numerator after multiplying
anonymous
  • anonymous
why isn't it multiplied by the bottom?
jim_thompson5910
  • jim_thompson5910
it is. I multiplied both top and bottom
jim_thompson5910
  • jim_thompson5910
|dw:1441002457520:dw|
anonymous
  • anonymous
is it |dw:1441002458990:dw|
jim_thompson5910
  • jim_thompson5910
the 2x+2h is incorrect
anonymous
  • anonymous
|dw:1441002630632:dw|
jim_thompson5910
  • jim_thompson5910
Yes you're on the right track. One more step and you'll get `h` as the simplified result in the numerator \[\Large (\color{red}{a}-\color{blue}{b})(\color{red}{a}+\color{blue}{b}) = \color{red}{a}^2 - \color{blue}{b}^2\] \[\Large (\color{red}{\sqrt{x+h}}-\color{blue}{\sqrt{x}})(\color{red}{\sqrt{x+h}}+\color{blue}{\sqrt{x}}) = (\color{red}{\sqrt{x+h}})^2 - (\color{blue}{\sqrt{x}})^2\] \[\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = x+h - x\] \[\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = h\]
jim_thompson5910
  • jim_thompson5910
so we'll have \[\Large \frac{x+h-x}{h(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{h}{h(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{\cancel{h}}{\cancel{h}(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{1}{\sqrt{x+h}+\sqrt{x}}\]
anonymous
  • anonymous
i'm going to try solving one on my own and can you check it to see if i'm doing it correctly?
jim_thompson5910
  • jim_thompson5910
sure that sounds like a good plan
anonymous
  • anonymous
would this be correct|dw:1441003416350:dw|
jim_thompson5910
  • jim_thompson5910
your steps and final answer are correct
anonymous
  • anonymous
alright thanks and could you help me with one last problem because i'm lost on it
jim_thompson5910
  • jim_thompson5910
sure
anonymous
  • anonymous
|dw:1441003887720:dw|
jim_thompson5910
  • jim_thompson5910
I'm guessing it wants you to rationalize the denominator?
anonymous
  • anonymous
i think so
jim_thompson5910
  • jim_thompson5910
then multiply top and bottom by the conjugate of the denominator
anonymous
  • anonymous
it doesn't specify all it says is simplify the radical expression
jim_thompson5910
  • jim_thompson5910
|dw:1441004360029:dw|
anonymous
  • anonymous
|dw:1441004288227:dw|
jim_thompson5910
  • jim_thompson5910
the denominator is correct but the numerator is not
jim_thompson5910
  • jim_thompson5910
you should have |dw:1441004582602:dw|
jim_thompson5910
  • jim_thompson5910
you have to FOIL it all out
anonymous
  • anonymous
|dw:1441004525342:dw|
jim_thompson5910
  • jim_thompson5910
correct
anonymous
  • anonymous
well bye have a good night and thank you very much for all your help i really appreciate it
jim_thompson5910
  • jim_thompson5910
you're welcome and good night

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