What is ((e^{2x})/x)(e^{-2x}) ?

The solution to ((e^{2x})/x)(e^{-2x}) is 1/x

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simplify ((e^{2x})/x)(e^{-2x})

simplify

(\frac{e ^{2 x}}{x}) (e^{- 2 x})

\frac{1}{x}

Solution steps

(\frac{e ^{2 x}}{x}) (e^{- 2 x})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{e ^{2 x}}{x} \cdot \frac{1}{e ^{2 x}}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{e ^{2 x} \cdot 1}{x e ^{2 x}}

Cancel the common factor:

e^{2 x}

= \frac{1}{x}

3 c i s (\frac{π}{4}) \cdot 5 c i s (\frac{π}{2})

t^{3} e^{- 2 t} sinh (4 t)

(5 r - 3)^{3}

e^{- l n (\frac{y}{x})}

- 4 X^{3} Y^{2 \circ} 5 X^{6} Y^{- 2 \circ} (- 8 X Y Z)