✔ 最佳答案
1)
1/(x - 1) + 2/(x + 1) = (x - 5) / (x² - 1)
( 1(x+1) + 2(x -1) ) / ( (x - 1)(x + 1) ) = (x - 5) / (x² - 1)
(3x - 1) / (x² - 1) = (x - 5) / (x² - 1)
3x - 1 = x - 5
x = - 2
2)
(x-1)/(x+1) + (x+8)/(x+2) - (x+9)/(x+3) - (x+2)/(x+4)
= (x+1 - 2)/(x+1) + (x+2 + 6)/(x+2) - (x+3 + 6)/(x+3) - (x+4 - 2)/(x+4)
= 1 - 2/(x+1) + 1 + 6/(x+2) - (1 + 6/(x+3)) - (1 - 2/(x+4))
= 1 - 2/(x+1) + 1 + 6/(x+2) - 1 - 6/(x+3) - 1 + 2/(x+4)
= 2/(x+4) - 2/(x+1) + 6/(x+2) - 6/(x+3)
= 2((x+1) - (x+4)) / ((x+1)(x+4)) + 6((x+3) - (x+2)) / ((x+2)(x+3))
= - 6 / ((x+1)(x+4)) + 6 / ((x+2)(x+3))
= ( - 6(x+2)(x+3) + 6(x+1)(x+4) ) / (x+1)(x+4) (x+2)(x+3)
= 6 ( (x+1)(x+4) - (x+2)(x+3) ) / ( (x+1) (x+2) (x+3) (x+4) )
= 6 ( (x²+5x+4) - (x²+5x+6) ) / ( (x+1) (x+2) (x+3) (x+4) )
= 6 ( - 2 ) / ( (x+1) (x+2) (x+3) (x+4) )
= - 12 / ( (x+1) (x+2) (x+3) (x+4) )