erweitern (1/2)(x^2+*+1)^{(-1)/2}(2x+1)

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (\frac{1}{2}) (x^{2} + + 1)^{\frac{- 1}{2}}, b = 2 x, c = 1

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

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

Vereinfache

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

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

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