What is expand (x+6)e^{1/x} ?

The solution to expand (x+6)e^{1/x} is e^{1/x}x+6e^{1/x}

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expand (x+6)e^{1/x}

expand

(x + 6) e^{\frac{1}{x}}

e^{\frac{1}{x}} x + 6 e^{\frac{1}{x}}

Solution steps

(x + 6) e^{\frac{1}{x}}

= e^{\frac{1}{x}} (x + 6)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{\frac{1}{x}}, b = x, c = 6

= e^{\frac{1}{x}} x + e^{\frac{1}{x}} \cdot 6

= e^{\frac{1}{x}} x + 6 e^{\frac{1}{x}}

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What is expand (x+6)e^{1/x} ?
The solution to expand (x+6)e^{1/x} is e^{1/x}x+6e^{1/x}