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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

u - 1

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

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

(1 - k)^{2}

5 m + 9 m + 13 - n - 7

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

8^{12} \cdot (8^{7})^{- 2}

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