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2.分式的加减第1课时分式的加减1.若xx2-1-=11-x2,则等于(D)(A)x1-x (B)xx-1 (C)1x+1 (D)1x-12.计算1x+12x+13x的结果为(D)(A)12x (B)16x (C)56x (D)116x3.化简a2-b2ab-ab-b2ab-a2等于(B)(A)ba(B)ab(C)-ba(D)-ab4.化简:a2a-b+2ab-b2b-a的结果是a-b.5.化简:x2x+1-1x+1+1=x.6.若9x+9x2-9=Ax+3+Bx-3,则A=3,B=6.7.计算:(1)aa2-1-11-a2;(2)1x+y-1x-y+2xx2-y2;(3)12m2-9+23-m.解:(1)aa2-1-11-a2=aa2-1+1a2-1=a+1a2-1=a+1(a+1)(a-1)=1a-1.(2)1x+y-1x-y+2xx2-y2=1x+y-1x-y+2x(x+y)(x-y)=(x-y)-(x+y)+2x(x+y)(x-y)=2x-2y(x+y)(x-y)=2(x-y)(x+y)(x-y)=2x+y.(3)12m2-9+23-m=12(m+3)(m-3)-2m-3=12(m+3)(m-3)-2(m+3)(m+3)(m-3)=12-2(m+3)(m+3)(m-3)=-2(m-3)(m+3)(m-3)=-2m+3.8.(xx广州)已知T=a2-9a(a+3)2+6a(a+3).(1)化简T;(2)若正方形ABCD的边长为a,且它的面积为9,求T的值.解:(1)T=a2-9a(a+3)2+6a(a+3)=a2-9a(a+3)2+6(a+3)a(a+3)2=a2-9+6(a+3)a(a+3)2=a2-9+6a+18a(a+3)2=(a+3)2a(a+3)2=1a.(2)因为正方形ABCD的边长为a,面积为9,所以a2=9,所以a=3(负值已舍去),所以T=1a=13.9.(规律探索题)(xx安徽)观察以下等式:第1个等式:11+02+1102=1,第2个等式:12+13+1213=1,第3个等式:13+24+1324=1,第4个等式:14+35+1435=1,第5个等式:15+46+1546=1,按照以上规律,解决下列问题:(1)写出第6个等式:;(2)写出你猜想的第n个等式:(用含n的等式表示),并证明.解:(1)16+57+1657=1.(2)1n+n-1n+1+1nn-1n+1=1.证明如下:因为左边=1n+n-1n+1+1nn-1n+1=n+1+n(n-1)+n-1n(n+1)=n(n+1)n(n+1)=1,右边=1,所以左边=右边,所以等式成立.所以第n个等式为1n+n-1n+1+1nn-1n+1=1.
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