初二数学问题(1）先化简,再求值.2x/x^2-y^2 +x/y^2-x^2 +y/(x-y)(x+y),其中x=-3,y=4（2）已知3x-4/(x-1)(x-2)=A/x-1 +B/x-2,求整式A,B
2019-05-23
初二数学问题
(1）先化简,再求值.
2x/x^2-y^2 +x/y^2-x^2 +y/(x-y)(x+y),其中x=-3,y=4
（2）已知3x-4/(x-1)(x-2)=A/x-1 +B/x-2,求整式A,B
优质解答
2x/x^2-y^2 +x/y^2-x^2 +y/(x-y)(x+y)
=x/(x-y)(x+y)+y/(x-y)(x+y)
=1/(x-y)
代入计算：原式=1/（-3-4）=-1/7
2、A/x-1 +B/x-2
=A(x-2)+B(x-1)/(x-1)(x-2)
=x(A+B)-2A-B
=3x-4/(x-1)(x-2)
所以A+B=3
-2A-B=-4
得A=1,B=2
2x/x^2-y^2 +x/y^2-x^2 +y/(x-y)(x+y)
=x/(x-y)(x+y)+y/(x-y)(x+y)
=1/(x-y)
代入计算：原式=1/（-3-4）=-1/7
2、A/x-1 +B/x-2
=A(x-2)+B(x-1)/(x-1)(x-2)
=x(A+B)-2A-B
=3x-4/(x-1)(x-2)
所以A+B=3
-2A-B=-4
得A=1,B=2