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

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

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

expand

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

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

Solution steps

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

Convert element to fraction:

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

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

Least Common Multiplier of

x + 1, x - 1, 1 : (x + 1) (x - 1)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

(x + 1) (x - 1) : x^{2} - 1

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

Expand

x (x - 1) - (x + 1) + ln (x + 1) (x + 1) (x - 1) : x^{2} - 2 x - 1 + x^{2} ln (x + 1) - ln (x + 1)

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

\frac{2}{( x + 3 ) ^{2}}

5 + (5 (1 - e)) e^{- x}

(- e^{t} cos (t) - sin (t))^{2}

\frac{1}{( x + 1 ) ( y + 1 )}

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

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