Question

第一题x+y+x-y分之y2第二题x2-3x+2分之1+x2-5x+6分之1+x2-4x+3分之1第三题1-x分之1+1

Answer 1

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)