1、提分专练(一)整式及分式的化简求值|类型1|整式的化简及求值1.2019湖州化简:(a+b)2-b(2a+b).2.2018襄阳先化简,再求值:(x+y)(x-y)+y(x+2y)-(x-y)2,其中x=2+3,y=2-3.|类型2|分式的化简及求值3.2019宜春联考先化简,再求值:3a-3aa2-2a+1a2-aa-1,其中a=2.4.2019绵阳先化简,再求值:aa2-b2-1a+bbb-a,其中a=2,b=2-2.5.2019黄石先化简,再求值:3x+2+x-2x2-2x+1x+2,其中|x|=2.6.2019枣庄先化简,再求值:x2x2-11x-1+1,其中,x为整数且满足不等式组x
2、-11,5-2x-2.【参考答案】1.解:原式=a2+2ab+b2-2ab-b2=a2.2.解:(x+y)(x-y)+y(x+2y)-(x-y)2=x2-y2+xy+2y2-x2+2xy-y2=3xy.当x=2+3,y=2-3时,原式=3(2+3)(2-3)=3.3.解:原式=3(a-1)aa2(a-1)2-aa-1=3aa-1-aa-1=2aa-1.当a=2时,原式=2aa-1=222-1=4.4.解:原式=a(a+b)(a-b)b-ab-1a+bb-ab=-ab(a+b)-b-ab(a+b)=-bb(a+b)=-1a+b,当a=2,b=2-2时,原式=-12+2-2=-12.5.解:原式=x2-1x+2(x-1)2x+2=(x+1)(x-1)x+2x+2(x-1)2=x+1x-1.|x|=2,x=2,由分式有意义的条件可知x=2,原式=3.6.解:原式=x2(x+1)(x-1)1+x-1x-1=x2(x+1)(x-1)x-1x=xx+1.解不等式组x-11,5-2x-2得2x72,因为x为整数,所以x=3.当x=3时,原式=xx+1=33+1=34.
