Thread: Can I simply e^3x/e^2x ?

1. Can I simply e^3x/e^2x ?

If I have:

$\displaystyle y = \frac{e^3x + 4}{e^2x}$

Can I simply as you would eg with x^3/x^2?

Can I call it:

$\displaystyle y = e^x + \frac{4}{e^2x}$

What are the rules in simplifying these? Or can you not?

Angus

2. Re: Can I simply e^3x/e^2x ?

Originally Posted by angypangy
If I have:

$\displaystyle y = \frac{e^3x + 4}{e^2x}$

Can I simply as you would eg with x^3/x^2?

Can I call it:

$\displaystyle y = e^x + \frac{4}{e^2x}$

What are the rules in simplifying these? Or can you not?

Angus
1. I assume that you mean $\displaystyle y = \frac{e^{3x} + 4}{e^{2x}}$

2. Re-write the RHS as a product

$\displaystyle y = \frac{e^{3x} + 4}{e^{2x}}=\left( e^{3x} + 4 \right) \cdot \frac1{e^{2x}}$

3. Expand the RHS and cancel equal factors:

$\displaystyle \left( e^{3x} + 4 \right) \cdot \frac1{e^{2x}} = \frac{e^{3x}}{e^{2x}} + \frac4{e^{2x}}$

3. Re: Can I simply e^3x/e^2x ?

Or write it as: $\displaystyle \left(e^{3x}+ 4\right)e^{-2x}= e^{3x- 2x}+ 4e^{-2x}= e^{x}+ 4e^{-2x}$.

4. Re: Can I simply e^3x/e^2x ?

Originally Posted by HallsofIvy
Or write it as: $\displaystyle \left(e^{3x}+ 4\right)e^{-2x}= e^{3x- 2x}+ 4e^{-2x}= e^{x}+ 4e^{-2x}$.
That's what I thought but I put both into my TI calculator and it seemed to give different graphs. I must have done something wrong because they are the same now.