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

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

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

simplify

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

\frac{x ^{2} - x + 1}{x ^{2} + x + 1}

Solution steps

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

Factor

x^{4} - x^{3} + x - 1 : (x - 1) (x + 1) (x^{2} - x + 1)

= \frac{( x - 1 ) ( x + 1 ) ( x ^{2} - x + 1 )}{x ^{4} + x ^{3} - x - 1}

Factor

x^{4} + x^{3} - x - 1 : (x + 1) (x - 1) (x^{2} + x + 1)

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

Cancel the common factor:

x - 1

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

Cancel the common factor:

x + 1

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

\frac{\frac{11 - w}{30 w ^{2}}}{\frac{w - 11}{5 w ^{6}}}

\frac{8 a ^{3} + 27}{4 a ^{2} + 12 a + 9}

\frac{cos ( x )}{sin ( x )} + \frac{sin ( x )}{1 + cos ( x )}

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

(5 x y + 14 x + 6 y) - (8 x - 4 y + 2 x y)

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