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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Multiply:

1 \cdot x^{\frac{1}{x} - 2} = x^{\frac{1}{x} - 2}

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

\frac{5 - x}{x ( x - 3 )}

(2 x + 7)^{2} π

\frac{1}{s ( s + a ) ( s + b )}

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

(k + 1)! \cdot (k + 2) - 1

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