2:
a)x / 2x+2 + x / 3x-3 + -x / 1-x2
= x / 2(x+1) + x / 3(x-1) + x / x2-1
= x(x-1) / 2(x+1)(x-1) + x(x+1) / 3(x-1)(x+1) + x / (x-1)(x+1)
= 3x(x-1) / 6(x+1)(x-1) + 2x(x+1) / 6(x+1)(x-1) + 6x / 6(x+1)(x-1)
= 3x(x-1) + 2x(x+1) + 6x / 6(x+1)(x-1)
= 3(x2-x) + 2(x2+x) + 6x / 6(x+1)(x-1)
= 3x2 - 3x + 2x2 + 2x + 6x / 6(x+1)(x-1)
= 5x2 + 5x / 6(x+1)(x-1)
= 5x(x+1) / 6(x+1)(x-1)
= 5x / 6(x-1) = 5(x-1) + 5 / 6(x-1)
= 5(x-1) / 6(x-1) + 5 / 6(x-1)
= 5/6 + 5 / 6(x-1)
b)x2-5x / x3+1 + x+2 / x2-x+1 + 1 / x+1
= x2-5x / x3+1 + (x+2)(x+1)+x2-x+1 / (x2-x+1)(x+1)
= x2-5x / x3+1 + x2+3x+2+x2-x+1 / x3+1
= x2-5x+x2+3x+2+x2-x+1 / x3+1
= 3x2-3x+3 / (x2-x+1)(x+1)
= 3(x2-x+1) / (x2-x+1)(x+1) = 3 / x+1