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受欢迎的代数 >

展开 (x-1)^{-1}-(x+3)^{-1}

解答

展开

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

解答

\frac{4}{x ^{2} + 2 x - 3}

求解步骤

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

使用指数法则:

a^{- 1} = \frac{1}{a}

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

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

使用指数法则:

a^{- 1} = \frac{1}{a}

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

= \frac{1}{x - 1} - \frac{1}{x + 3}

x - 1, x + 3

的最小公倍数:

(x - 1) (x + 3)

根据最小公倍数调整分式

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

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

乘开

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

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

乘开

x + 3 - (x - 1) : 4

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

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