What is ((x^6-1))/((x-1)) ?

The solution to ((x^6-1))/((x-1)) is (x+1)(x^2+1+x)(x^2+1-x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((x^6-1))/((x-1))

simplify

\frac{( x ^{6} - 1 )}{( x - 1 )}

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

Solution steps

\frac{x ^{6} - 1}{x - 1}

Apply exponent rules

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

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x^{2})^{3} - 1^{3} = (x^{2} - 1) (x^{4} + x^{2} + 1)

= \frac{( x ^{2} - 1 ) ( x ^{4} + x ^{2} + 1 )}{x - 1}

Factor

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

= \frac{( x + 1 ) ( x - 1 ) ( x ^{4} + x ^{2} + 1 )}{x - 1}

Factor

x^{4} + x^{2} + 1 : (x^{2} + 1 + x) (x^{2} + 1 - x)

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

Cancel the common factor:

x - 1

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

\frac{12}{99}

85 + 115

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

(1 + i)^{2} (1 - i)^{2}

9 y - (9.4 z + 3)

What is ((x^6-1))/((x-1)) ?
The solution to ((x^6-1))/((x-1)) is (x+1)(x^2+1+x)(x^2+1-x)