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)

(x + 2)^{8}

1 + 3.322 lo g_{10} (20)

\frac{x ^{2} - 64}{x ^{2} - 9 x} \cdot \frac{x + 9}{x ^{2} + x - 72}

i^{129}

i^{225}