# Math Help - Simplifying with exponents

1. ## Simplifying with exponents

Mr. Math Book says that

$\frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^{2x}+1}{e^{2x}-1}$

Can someone tell me how the LHS was simplified?? Thx

2. $\displaystyle \frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^x+\frac{1}{e^x}}{e^x-\frac{1}{e^x}}=\frac{\frac{e^{2x}+1}{e^x}}{\frac{e ^{2x}-1}{e^x}}=\frac{e^{2x}+1}{e^{2x}-1}$

3. Hello, DivideBy0!

Another way . . .

$\frac{e^x+e^{-x}}{e^x-e^{-x}}=\frac{e^{2x}+1}{e^{2x}-1}$
Multiply by $\frac{e^x}{e^x}$

. . $\frac{e^x}{e^x}\cdot\frac{e^x+e^{-x}}{e^x-e^{-x}} \;=\;\frac{e^{2x} + 1}{e^{2x} - 1}$