1. ## Algebraic Simplification

Okay I've got this:

$\displaystyle y-\sqrt{2}=(y+\sqrt{2})Ce^{-\sqrt{2}x^2}$

and need to make it so that

$\displaystyle y=\frac{\sqrt{2}(1+Ce^{-\sqrt{2}x^2})}{1-Ce^{-\sqrt{2}x^2}}$

Where C is just a constant

Need helps with then steps involved please...

2. ## Re: Algebraic Simplification

Well, do it. What's your first step?

3. ## Re: Algebraic Simplification

Sorry I've no idea lol. Maybe add $\displaystyle \sqrt{2}$ to both sides and try to do something from there? I'm sorry im clueless lol. Sorry if this is supposed to be easy :S

4. ## Re: Algebraic Simplification

\displaystyle \displaystyle \begin{align*}y - \sqrt{2} &= \left(y + \sqrt{2}\right)Ce^{-\sqrt{2}x^2} \\ y - \sqrt{2} &= Cye^{-\sqrt{2}x^2} + C\sqrt{2}e^{-\sqrt{2}x^2} \\ y - Cye^{-\sqrt{2}x^2} &= \sqrt{2} + C\sqrt{2}e^{-\sqrt{2}x^2} \\ y\left(1 - Ce^{-\sqrt{2}x^2}\right) &= \sqrt{2}\left(1 + Ce^{-\sqrt{2}x^2}\right) \end{align*}

Finish it.

5. ## Re: Algebraic Simplification

Originally Posted by Prove It
\displaystyle \displaystyle \begin{align*}y - \sqrt{2} &= \left(y + \sqrt{2}\right)Ce^{-\sqrt{2}x^2} \\ y - \sqrt{2} &= Cye^{-\sqrt{2}x^2} + C\sqrt{2}e^{-\sqrt{2}x^2} \\ y - Cye^{-\sqrt{2}x^2} &= \sqrt{2} + C\sqrt{2}e^{-\sqrt{2}x^2} \\ y\left(1 - Ce^{-\sqrt{2}x^2}\right) &= \sqrt{2}\left(1 + Ce^{-\sqrt{2}x^2}\right) \end{align*}

Finish it.
Whoa!!! Multiply out, then take the common factors of $\displaystyle \sqrt2$ and y!! You're a genious!!!!!!!

Edit: I'm probably actually just stupid lol, but the former is probably also true!

6. ## Re: Algebraic Simplification

Originally Posted by Umair
Whoa!!! Multiply out, then take the common factors of $\displaystyle \sqrt2$ and y!! You're a genious!!!!!!!

Edit: I'm probably actually just stupid lol, but the former is probably also true!
Don't call yourself stupid, you'll start believing it ><

I think you also mean "Genius", not "Genious" :P

7. ## Re: Algebraic Simplification

Originally Posted by Umair
I've no idea lol.
Please see how catastrophic this is. GET an idea. No idea never will be funny. Pay attention in class. Read the material. You WILL have SOME idea.

Never say or think that again.