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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 1

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

(- 5 x) (4 x)

16 \times 3

(x + 7) (x + 5)

(- 10 x^{2} + 9) + (8 x^{2} - 5 x + 7)

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