## anonymous one year ago Help please

1. anonymous

|dw:1441001669103:dw|

2. anonymous

3. jim_thompson5910

does it want you to apply a limit? or just simplify?

4. anonymous

just simplify

5. jim_thompson5910

ok like before, multiply top and bottom by $$\Large \sqrt{x+h}+\sqrt{x}$$ $\Large \frac{\sqrt{x+h}-\sqrt{x}}{h}$ $\Large \frac{(\sqrt{x+h}-\sqrt{x})}{h}\times \color{red}{\frac{(\sqrt{x+h}+\sqrt{x})}{(\sqrt{x+h}+\sqrt{x})}}$

6. jim_thompson5910

tell me what you get in the numerator after multiplying

7. anonymous

why isn't it multiplied by the bottom?

8. jim_thompson5910

it is. I multiplied both top and bottom

9. jim_thompson5910

|dw:1441002457520:dw|

10. anonymous

is it |dw:1441002458990:dw|

11. jim_thompson5910

the 2x+2h is incorrect

12. anonymous

|dw:1441002630632:dw|

13. jim_thompson5910

Yes you're on the right track. One more step and you'll get h as the simplified result in the numerator $\Large (\color{red}{a}-\color{blue}{b})(\color{red}{a}+\color{blue}{b}) = \color{red}{a}^2 - \color{blue}{b}^2$ $\Large (\color{red}{\sqrt{x+h}}-\color{blue}{\sqrt{x}})(\color{red}{\sqrt{x+h}}+\color{blue}{\sqrt{x}}) = (\color{red}{\sqrt{x+h}})^2 - (\color{blue}{\sqrt{x}})^2$ $\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = x+h - x$ $\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = h$

14. jim_thompson5910

so we'll have $\Large \frac{x+h-x}{h(\sqrt{x+h}+\sqrt{x})}$ $\Large \frac{h}{h(\sqrt{x+h}+\sqrt{x})}$ $\Large \frac{\cancel{h}}{\cancel{h}(\sqrt{x+h}+\sqrt{x})}$ $\Large \frac{1}{\sqrt{x+h}+\sqrt{x}}$

15. anonymous

i'm going to try solving one on my own and can you check it to see if i'm doing it correctly?

16. jim_thompson5910

sure that sounds like a good plan

17. anonymous

would this be correct|dw:1441003416350:dw|

18. jim_thompson5910

19. anonymous

alright thanks and could you help me with one last problem because i'm lost on it

20. jim_thompson5910

sure

21. anonymous

|dw:1441003887720:dw|

22. jim_thompson5910

I'm guessing it wants you to rationalize the denominator?

23. anonymous

i think so

24. jim_thompson5910

then multiply top and bottom by the conjugate of the denominator

25. anonymous

it doesn't specify all it says is simplify the radical expression

26. jim_thompson5910

|dw:1441004360029:dw|

27. anonymous

|dw:1441004288227:dw|

28. jim_thompson5910

the denominator is correct but the numerator is not

29. jim_thompson5910

you should have |dw:1441004582602:dw|

30. jim_thompson5910

you have to FOIL it all out

31. anonymous

|dw:1441004525342:dw|

32. jim_thompson5910

correct

33. anonymous

well bye have a good night and thank you very much for all your help i really appreciate it

34. jim_thompson5910

you're welcome and good night