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

The solution to (x-2)/(x^2)+(x+2)/(x^2-x)-1/(x^2-1) is (2x^3+x+2)/(x^2(x-1)(x+1))

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

simplify

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

\frac{2 x ^{3} + x + 2}{x ^{2} ( x - 1 ) ( x + 1 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - 2) (x - 1) (x + 1) + (x + 2) x (x + 1) - x^{2} : 2 x^{3} + x + 2

= \frac{2 x ^{3} + x + 2}{x ^{2} ( x - 1 ) ( x + 1 )}

(x - 10) (x - 3)

\frac{x ^{- 3}}{- 3}

2^{3} \times 2^{2}

\frac{3 x ^{4} y}{27 x ^{8} y}

x^{2} - 250 x + 15000

What is (x-2)/(x^2)+(x+2)/(x^2-x)-1/(x^2-1) ?
The solution to (x-2)/(x^2)+(x+2)/(x^2-x)-1/(x^2-1) is (2x^3+x+2)/(x^2(x-1)(x+1))