What is 1/(x-1)+1/((x-1)^2)+x/(x^2-1) ?

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

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simplify 1/(x-1)+1/((x-1)^2)+x/(x^2-1)

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

1 0^{- 6} \cdot 1 0^{- 6}

3 x e^{\frac{1}{2} x} d x

- 13 y^{4} (- 14 x^{3} y)

\frac{a + bi}{c + d i}

3 \frac{1}{6} - 1 \frac{1}{2} + \frac{1}{3}

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