化简 (1+\frac{x+1)/(x-1)}{1/(x-1)-1/(x+1)}

解答

化简

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

x (x + 1)

求解步骤

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

合并

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

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

合并

\frac{1}{x - 1} - \frac{1}{x + 1} : \frac{2}{( x - 1 ) ( x + 1 )}

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

使用分式法则:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

消掉

\frac{2 x ( x - 1 ) ( x + 1 )}{( x - 1 ) \cdot 2} : x (x + 1)

= x (x + 1)

e x p an d (3 x + 7) (2 x - 10)

s im pl i f y \frac{7 y - 14}{y ^{2} - 7 y + 10} + \frac{10}{y - 5}

s im pl i f y \frac{6 y ^{- 1}}{6 x y}

e x p an d 4 k^{2} (- 3 k^{2} - 4 k + 5)

s im pl i f y \frac{7}{x} - \frac{5}{y}