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

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

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

simplify

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Two Squares Formula:

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

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

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

Factor

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

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

Cancel the common factor:

x - 1

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

1 \cdot 0

\frac{16}{48}

x x

\frac{1}{4} \times \frac{1}{2}