What is expand (1/2)(x^2+*+1)^{(-1)/2}(2x+1) ?

The solution to expand (1/2)(x^2+*+1)^{(-1)/2}(2x+1) is x/((x^2+1)^{1/2)}+1/(2(x^2+1)^{1/2)}

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

expand

(\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}}}

Solution steps

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

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

Apply the distributive law:

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}}

Simplify

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}}}

5 (e^{7 x - 7 y} + 7 e^{7 x - 7 y} x)

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

\frac{1}{2 ( 2 n + 4 + 6 m )}

(2 x - 2) (H (t - 1) - H (t - 4))

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

What is expand (1/2)(x^2+*+1)^{(-1)/2}(2x+1) ?
The solution to expand (1/2)(x^2+*+1)^{(-1)/2}(2x+1) is x/((x^2+1)^{1/2)}+1/(2(x^2+1)^{1/2)}