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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

lo g_{0.01} (10)

\frac{a ^{2} - ab}{ab - b ^{2}}

\frac{1}{x} + \frac{2 x}{5}

\frac{- 6}{x}

- 2 x^{3} + 12 x^{2} - 16 x

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