What is e^{-1/2 ln|x^2+2x-1|} ?

The solution to e^{-1/2 ln|x^2+2x-1|} is 1/(sqrt(|x^2+2x-1|))

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simplify e^{-1/2 ln|x^2+2x-1|}

simplify

e^{- \frac{1}{2} l n ∣ x^{2} + 2 x - 1 ∣}

\frac{1}{∣ x ^{2} + 2 x - 1 ∣}

Solution steps

e^{- \frac{1}{2} l n ∣ x^{2} + 2 x - 1 ∣}

Apply exponent rule:

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

= \frac{1}{e ^{\frac{1}{2} l n ∣ x^{2} + 2 x - 1 ∣}}

e^{\frac{1}{2} l n ∣ x^{2} + 2 x - 1 ∣} = ∣ x^{2} + 2 x - 1 ∣

= \frac{1}{∣ x ^{2} + 2 x - 1 ∣}

(e^{x} + 1)^{- 1}

4 + 15 \cdot 4 - 15

(3 + 5 x)^{- 3}

20 (\frac{1}{2} x 16 - \frac{1}{4} x^{2})

x x^{\frac{3}{2}}

What is e^{-1/2 ln|x^2+2x-1|} ?
The solution to e^{-1/2 ln|x^2+2x-1|} is 1/(sqrt(|x^2+2x-1|))