數學有理函數問題？

1. 3/(2a+b) - (6a+7b)/(b^2-4a^2) + 5/(b-2a)
= 3/(2a+b) - (6a+7)/(b-2a)(b+2a) + 5/(b-2a)
= [3(b-2a) - (6a+7) + 5(b+2a)]/(b-2a)(b+2a)
= (3b-6a-6a-7+5b+10a)/(b-2a)(b+2a)
= (8b-2a+7)/(b-2a)(b+2a)
2. x/(2x+3y)(x-1) -
3y/(3y+2)(3y+2x) + 1/(1-x)(3y+2)
= x/(2x+3y)(x-1) - 3y/(3y+2)(3y+2x) - 1/(x-1)(3y+2)
= [x(3y+2) - 3y(x-1) - 1(2x+3y)]/(2x+3y)(x-1)(3y+2)
= (3xy + 2x - 3xy + 3y - 2x - 3y)/(2x+3y)(x-1)(3y+2)

= 0
3.x+1/x * 2x^2-3x+1/x-1 -
(x^2-1/2x-4) / (x-1/x^2-1)
= [(x+1)(2x^2 -3x +1)]/x(x-1) - (x^2 -1)(x^2-1)/2(x-2)(x-1)
= (x+1)(x-1)(2x-1)/x(x-1) - (x-1)(x+1)(x-1)(x+1)/2(x-2)(x-1)
= (x+1)(2x-1)/x - (x+1)(x+1)(x-1)/2(x-2)
= [2(x+1)(2x-1)(x-2) - x(x+1)(x+1)(x-1)] /2x(x-2)
= (x+1)[2(2x^2 -5x + 2) - x(x^2 - 1)] / 2x(x-2)
= (x+1)(4x^2 - 10x + 4 - x^3 + x)/2x(x-2)
= (x+1)(-x^3 + 4x^2 - 9x + 4)/2x(x-2)