1. JacksonJRB

$y=\sqrt{\frac{ 4x-1 }{ x }}$

2. JacksonJRB

Every new problem I look at seems to make less and less sense.

3. SolomonZelman

$$\large\color{black}{ \displaystyle y^2=\frac{4x-1}{x} }$$ $$\large\color{black}{ \displaystyle y^2=\frac{4x}{x}-\frac{1}{x} }$$ $$\large\color{black}{ \displaystyle y^2=4-\frac{1}{x} }$$ can you take it from there?

4. SolomonZelman

all they are asking you to do, is to isolate the x (without performing incorrect operations).

5. JacksonJRB

$x=\frac{ -1 }{ y^2-4 }$

6. SolomonZelman

yes, and if you want you can simplify that just a bit, to get: $$\large\color{black}{ \displaystyle x=\frac{1}{4-y^2} }$$

7. JacksonJRB

Ah, thanks again

8. SolomonZelman

You are always welcome

9. JacksonJRB

There is another one that I will try on my own for now but I'll ask if I need help again

10. SolomonZelman

Ok:)

11. JacksonJRB

$y=\frac{ 1 }{ x^2+2x }$ $x^2+2x=\frac{ 1 }{ y }$

12. SolomonZelman

the second equation is the next step that you took?

13. JacksonJRB

Yes

14. SolomonZelman

Ok, you can subtract -1/y from both sides, and do the quadratic formula. a=1 b=2 c=1/y

15. SolomonZelman

i mean c=-1/y

16. JacksonJRB

Ah, ok

17. JacksonJRB

ill try that

18. SolomonZelman

$$\large\color{black}{ \displaystyle x^2+2x\color{red}{-\frac{1}{y}}=\frac{1}{y}\color{red}{-\frac{1}{y}} }$$ $$\large\color{black}{ \displaystyle x^2+2x-\frac{1}{y}=0 }$$

19. SolomonZelman

go on... :)

20. JacksonJRB

$x=\frac{ -2+/-\sqrt{4+\frac{ 4 }{ y }} }{ }$

21. JacksonJRB

over 2

22. SolomonZelman

you can do a $$\pm$$ sign in latex by \pm (just a code advise) and yes, so far correct

23. JacksonJRB

$x=-2\pm \sqrt{4y+4}$

24. JacksonJRB

over 2 again

25. SolomonZelman

i don't think I followed you this time. How come your y came from denominator to numerator?

26. SolomonZelman

$$\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4-4(1)(-\frac{1}{y})}}{2} }$$ $$\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4+4(\frac{1}{y})}}{2} }$$ it should be like this

27. JacksonJRB

ah

28. SolomonZelman

it can be simplified ....

29. SolomonZelman

$$\large\color{black}{ \displaystyle x=\frac{-2\pm\sqrt{4+4(\frac{1}{y})}}{2} }$$ $$\large\color{black}{ \displaystyle x=\frac{-2\pm2\sqrt{1+(\frac{1}{y})}}{2} }$$ $$\large\color{black}{ \displaystyle x=-1\pm\sqrt{1+\frac{1}{y}} }$$

30. SolomonZelman

this is it, technically, although, if you feel like or need to you can rationalize the denominator

31. JacksonJRB

Don't think do

32. JacksonJRB

Thank you so much

33. JacksonJRB

*think so

34. SolomonZelman

yw