化简 (x^4-x^3+x-1)/(x^4+x^3-x-1)

解答

化简

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

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

求解步骤

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

因式分解

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}

因式分解

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 )}

约分:

x - 1

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

约分:

x + 1

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

s im pl i f y \frac{\frac{11 - w}{30 w ^{2}}}{\frac{w - 11}{5 w ^{6}}}

s im pl i f y \frac{cos ( x )}{sin ( x )} + \frac{sin ( x )}{1 + cos ( x )}

s im pl i f y (3^{- 1} + 3^{- 2})^{- 1}

s im pl i f y (5 x y + 14 x + 6 y) - (8 x - 4 y + 2 x y)

s im pl i f y 3 + \frac{1}{3} - \frac{1}{12} - (1 - (2 \frac{1}{4} + 1.7))