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)

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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)

- 16 x - [5 x + 7 (- 3 x + 2)]

8 - 60

(w + 7) (w + 3)

8 (x + 5) - 4 (x + 4)

\frac{3 x - 6 + a x - 2 a}{x - 2}

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)