1
x+y+y²/(x-y)
=[(x+y)(x-y)+y²]/(x-y)
=[x²-y²+y²]/(x-y)
=x²/(x-y)
2
1/(x²-3x+2)+1/(x²-5x+6)+1/(x²-4x+3)
=1/[(x-1)(x-2)]+1/[(x-2)(x-3)]+1/[(x-1)(x-3)]
=[(x-3)+（x-1)+（x-2)]/[(x-1)(x-2)(x-3)]
=(3x-6)/[(x-1)(x-2)(x-3)]
3
1/(1-x)+1/(1+x)+2/(1+x²)+4/(1+x^4)
=[(1+x)+(1-x)]/[(1-x)(1+x)]+2/(1+x²)+4/(1+x^4)
=2/(1-x²)+2/(1+x²)+4/(1+x^4)
=2[(1+x²)+(1-x²)]/(1-x^4)+4/(1+x^4)
=4/(1-x^4)+4/(1+x^4)
=4[(1+x^4)+(1-x^4)]/(1-x^8)
=8/(1-x^8)
4
m-2=(m²-4)/(m+2)