化简 1/2 (x+pi)^{-1/2}(x+pi) 1/(1-x^2)

解答

化简

\frac{1}{2} (x + π)^{- \frac{1}{2}} (x + π) \frac{1}{1 - x ^{2}}

\frac{( x + π ) ^{\frac{1}{2}}}{2 ( - x ^{2} + 1 )}

求解步骤

\frac{1}{2} (x + π)^{- \frac{1}{2}} (x + π) \frac{1}{1 - x ^{2}}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

(x + π)^{- \frac{1}{2}} (x + π) = (x + π)^{- \frac{1}{2} + 1}

= \frac{1}{2} (x + π)^{- \frac{1}{2} + 1} \frac{1}{1 - x ^{2}}

(x + π)^{- \frac{1}{2} + 1} = (x + π)^{\frac{1}{2}}

= \frac{1}{2} \cdot \frac{1}{- x ^{2} + 1} (x + π)^{\frac{1}{2}}

分式相乘:

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

= \frac{1 \cdot 1 \cdot ( x + π ) ^{\frac{1}{2}}}{2 ( 1 - x ^{2} )}

乘以:

1 \cdot 1 \cdot (x + π)^{\frac{1}{2}} = (x + π)^{\frac{1}{2}}

= \frac{( x + π ) ^{\frac{1}{2}}}{2 ( - x ^{2} + 1 )}

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