展开 (a^2-1)/a-1/(a-1)

解答

展开

\frac{a ^{2} - 1}{a} - \frac{1}{a - 1}

\frac{a ^{3} - a ^{2} - 2 a + 1}{a ^{2} - a}

求解步骤

\frac{a ^{2} - 1}{a} - \frac{1}{a - 1}

a, a - 1

的最小公倍数:

a (a - 1)

根据最小公倍数调整分式

= \frac{( a ^{2} - 1 ) ( a - 1 )}{a ( a - 1 )} - \frac{a}{a ( a - 1 )}

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{( a ^{2} - 1 ) ( a - 1 ) - a}{a ( a - 1 )}

乘开

a (a - 1) : a^{2} - a

= \frac{( a ^{2} - 1 ) ( a - 1 ) - a}{a ^{2} - a}

乘开

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

= \frac{a ^{3} - a ^{2} - 2 a + 1}{a ^{2} - a}

e x p an d - \frac{d}{d s} (\frac{e ^{- π s}}{s ( s ^{2} + 1 )})

e x p an d \frac{9 x ^{3} + 16 x ^{2} + 3 x - 10}{x ^{3} ( x + 5 )}

s im pl i f y (x + 1 + 2) (x + 1 - 2) (x^{2} + 7)

e x p an d (x + 2)^{2 (x - 1)}

e x p an d \frac{3 s ^{2} + 2 s + 1}{( s ^{2} + 1 ) ( s ^{2} + 2 s + 2 )}