\displaystyle\frac{e^x-1}{\sin x-\textrm{sh} 2x}=\displaystyle \frac{e^x-1}{\sin x-\textrm{sh} 2x}\cdot \frac{\frac{1}{x}}{\frac{1}{x}}=\frac{\frac{e^x-1}{x}}{\frac{\sin x-\textrm{sh} 2x}{x}}=\frac{1}{\frac{\sin x}{x}-2\frac{\textrm{sh} 2x}{2x}}=\frac{1}{1-2}=-1