What is expand ((2-x)(ln(1-x)))/x ?

The solution to expand ((2-x)(ln(1-x)))/x is (2ln(1-x))/x-ln(1-x)

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expand ((2-x)(ln(1-x)))/x

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

Expand

(2 - x) ln (1 - x) : 2 ln (1 - x) - x ln (1 - x)

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Cancel

\frac{x ln ( 1 - x )}{x} : ln (- x + 1)

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

e^{y} (\frac{d y}{d x} + 1) =!

\frac{( x - 2 ) ( 2 x + 3 )}{x + 47}

5 - 3 \cdot 2

\frac{9000 e ^{- 2 t} ( - e ^{t} + 9 )}{( 1 + 9 e ^{- t} ) ^{3}}

\frac{2 π ( e ^{5} - 1 )}{3 e}

What is expand ((2-x)(ln(1-x)))/x ?
The solution to expand ((2-x)(ln(1-x)))/x is (2ln(1-x))/x-ln(1-x)