Question

Simplify the expression. (Do not expand the expression in the denominator.)

(e^2x − e^−2x)^2 − (e^2x + e^−2x)^2
(e^2x + e^−2x)^2

Answer 1

\[\left( e ^{2x}-e ^{-2x} \right)^{2}-\left( e ^{2x}+e ^{-2x} \right)^{2}\]
________________
\[\left( e ^{2x}+e ^{-2x} \right)^{2}\]

Answer 2

Just to make it clearer

Answer 3

```
\[
\frac{(e^{2x}-e^{-2x})^2-(e^{2x}+e^{-2x})^2}{(e^{2x}+e^{-2x})^2}
\]
```
\[
\frac{(e^{2x}-e^{-2x})^2-(e^{2x}+e^{-2x})^2}{(e^{2x}+e^{-2x})^2}
\]

Answer 4

I figured it out just now! ^^;

Answer 5

Let \(a=e^{2x}-e^{-2x}\) and \(b=e^{2x}+e^{-2x}\)\[
\frac{a^2-b^2}{b^2}
\]

Answer 6

This is difference of squares.\[
\frac{a^2-b^2}{b^2}=\frac{(a-b)(a+b)}{b^2}
\]

Answer 7

I understand it now ^^;