3/((x-2)(x+1))-(1/(x-2))2/(a²-1)+1/(a+1)x/(2-x)-(4-x²)/(x²-4x+4)

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3/((x-2)(x+1))-(1/(x-2))2/(a²-1)+1/(a+1)x/(2-x)-(4-x²)/(x²-4x+4)
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3/((x-2)(x+1))-(1/(x-2))2/(a²-1)+1/(a+1)x/(2-x)-(4-x²)/(x²-4x+4)
3/((x-2)(x+1))-(1/(x-2))
2/(a²-1)+1/(a+1)
x/(2-x)-(4-x²)/(x²-4x+4)

3/((x-2)(x+1))-(1/(x-2))2/(a²-1)+1/(a+1)x/(2-x)-(4-x²)/(x²-4x+4)
3/((x-2)(x+1))-(1/(x-2)) =3/((x-2)(x+1))-(x+1)/(x-2)(x+1) =(3-x-1)/((x-2)(x+1) =(2-x)/(x-2)(x+1) =-1/(x+1) 2/(a²-1)+1/(a+1) =2/(a²-1)+(a-1)/(a+1)(a-1) =(2+a-1)/((a²-1) =(a+1)/((a²-1) =1/(a-1) x/(2-x)-(4-x²)/(x²-4x+4) =-x(x-2)/ (x²-4x+4)-(4-x²)/(x²-4x+4) =(-x²+2x-4+x²)/(x²-4x+4) =-2(x-2)/(x²-4x+4) =-2/(x-2) =2/(2-x)