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

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

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simplify (x+2)/(x^3-1)-1/(x-1)

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

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

50 x^{3}

\frac{3 x}{2 x}

55 - 25

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

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