What is (x^4-1)/(x^3-1) ?

The solution to (x^4-1)/(x^3-1) is ((x^2+1)(x+1))/(x^2+x+1)

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simplify (x^4-1)/(x^3-1)

simplify

\frac{x ^{4} - 1}{x ^{3} - 1}

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

Solution steps

\frac{x ^{4} - 1}{x ^{3} - 1}

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 1

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

(x - 2) (x - 3) (x - 4) (x - 5)

15 - 4 (\frac{3}{2} x + 8)

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

(\frac{3}{4} x^{2} y - \frac{1}{3} x z)^{2}

\frac{3}{4} \cdot \frac{2}{4}

What is (x^4-1)/(x^3-1) ?
The solution to (x^4-1)/(x^3-1) is ((x^2+1)(x+1))/(x^2+x+1)