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