What is ((3x+e^{2x}x)/2-1/4 e^{2x})e^{-2x} ?

The solution to ((3x+e^{2x}x)/2-1/4 e^{2x})e^{-2x} is (2(3x+e^{2x}x)-e^{2x})/(4e^{2x)}

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simplify ((3x+e^{2x}x)/2-1/4 e^{2x})e^{-2x}

simplify

(\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x}) e^{- 2 x}

\frac{2 ( 3 x + e ^{2 x} x ) - e ^{2 x}}{4 e ^{2 x}}

Solution steps

(\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x}) e^{- 2 x}

Apply exponent rule:

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

= \frac{1}{e ^{2 x}} (\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x})

Multiply fractions:

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

= \frac{1 \cdot ( \frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e ^{2 x} )}{e ^{2 x}}

1 \cdot (\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x}) = \frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x}

= \frac{\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e ^{2 x}}{e ^{2 x}}

Join

\frac{3 x + e ^{2 x} x}{2} - \frac{1}{4} e^{2 x} : \frac{2 ( 3 x + e ^{2 x} x ) - e ^{2 x}}{4}

= \frac{\frac{2 ( 3 x + e ^{2 x} x ) - e ^{2 x}}{4}}{e ^{2 x}}

Apply the fraction rule:

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

= \frac{( 3 x + e ^{2 x} x ) \cdot 2 - e ^{2 x}}{4 e ^{2 x}}

6 (1) (1) e^{3 (1)^{2} (1)} (1)^{2}

103 d d

What is ((3x+e^{2x}x)/2-1/4 e^{2x})e^{-2x} ?
The solution to ((3x+e^{2x}x)/2-1/4 e^{2x})e^{-2x} is (2(3x+e^{2x}x)-e^{2x})/(4e^{2x)}