Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[l\imath mx->e\times \frac{\sqrt[x-e]{x}}{\sqrt[x-e]{e}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[l\imath mx->{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}\]
Regroup terms.
\[-+l\imath mx>{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{\imath }\]
Rationalize the denominator: \(\frac{{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{\imath } \cdot \frac{\imath }{\imath }=-{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}\imath \).
\[-+lmx>-{e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}\imath \]
Regroup terms.
\[-+lmx>-\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}\]
Divide both sides by \(m\).
\[-+lx>-\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{m}\]
Divide both sides by \(x\).
\[-+l>-\frac{\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{m}}{x}\]
Simplify \(\frac{\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{m}}{x}\) to \(\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{mx}\).
\[-+l>-\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{mx}\]
Simplify \(\frac{\imath {e}^{1-\frac{1}{x-e}}\sqrt[x-e]{x}}{mx}\) to \(\frac{\imath {e}^{1-\frac{1}{x-e}}{x}^{\frac{1}{x-e}-1}}{m}\).
\[-+l>-\frac{\imath {e}^{1-\frac{1}{x-e}}{x}^{\frac{1}{x-e}-1}}{m}\]
Multiply both sides by \(-1\).
\[l<\frac{\imath {e}^{1-\frac{1}{x-e}}{x}^{\frac{1}{x-e}-1}}{m}\]
l<(IM*e^(1-1/(x-e))*x^(1/(x-e)-1))/m
