中考分式化簡(jiǎn)求值專項(xiàng)練習(xí)與答案一、中考分式化簡(jiǎn)求值專項(xiàng)練習(xí)先化簡(jiǎn)，再求值：(\frac{x}{x-1}-\frac{3}{x-1})\div\frac{x^2-9}{x-1}，其中x=2。化簡(jiǎn)求值：\frac{a^2-1}{a^2+2a+1}\div\frac{a-1}{a+1}+\frac{a}{a+1}，其中a=-2。先化簡(jiǎn)，再求值：(\frac{x^2}{x-2}+\frac{4}{2-x})\div\frac{x+2}{2x}，其中x=\frac{1}{2}。已知x^2-2x-3=0，求\frac{x^2-4x+4}{x^2-4}\div\frac{x-2}{x^2+2x}+3的值?；?jiǎn)并求值：\frac{m^2-6m+9}{m^2-9}\div(\frac{m-3}{m+3}-\frac{m-9}{m^2+6m+9})，其中m=\sqrt{3}-3。先化簡(jiǎn)，再求值：(\frac{1}{x+1}-\frac{1}{x-1})\div\frac{2}{1-x}，其中x=\sqrt{2}-1。已知a-b=2，ab=-1，求\frac{a^2-b^2}{a^2+ab}\div(a-\frac{2ab-b^2}{a})的值。化簡(jiǎn)求值：\frac{x^2-2x+1}{x^2-1}\div(\frac{x-1}{x+1}-x+1)，從-1，0，1，2中選一個(gè)合適的數(shù)作為x的值代入求值。先化簡(jiǎn)，再求值：\frac{a^2-4}{a^2+6a+9}\div\frac{a-2}{2a+6}-\frac{2}{a+3}，其中a=(\frac{1}{2})^{-2}-3^0。已知x^2+3x-1=0，求\frac{x^2}{x^4+x^2+1}的值。二、答案化簡(jiǎn)：先計(jì)算括號(hào)內(nèi)：(\frac{x}{x-1}-\frac{3}{x-1})=\frac{x-3}{x-1}。再將除法轉(zhuǎn)化為乘法，\frac{x-3}{x-1}\div\frac{x^2-9}{x-1}=\frac{x-3}{x-1}\times\frac{x-1}{(x+3)(x-3)}=\frac{1}{x+3}。求值：當(dāng)x=2時(shí)，\frac{1}{x+3}=\frac{1}{2+3}=\frac{1}{5}?；?jiǎn)：對(duì)分子分母進(jìn)行因式分解，\frac{a^2-1}{a^2+2a+1}=\frac{(a+1)(a-1)}{(a+1)^2}=\frac{a-1}{a+1}。原式變?yōu)閈frac{a-1}{a+1}\div\frac{a-1}{a+1}+\frac{a}{a+1}。將除法轉(zhuǎn)化為乘法，\frac{a-1}{a+1}\times\frac{a+1}{a-1}+\frac{a}{a+1}=1+\frac{a}{a+1}=\frac{a+1+a}{a+1}=\frac{2a+1}{a+1}。求值：當(dāng)a=-2時(shí)，\frac{2a+1}{a+1}=\frac{2\times(-2)+1}{-2+1}=\frac{-4+1}{-1}=3?；?jiǎn)：括號(hào)內(nèi)變形：\frac{x^2}{x-2}+\frac{4}{2-x}=\frac{x^2}{x-2}-\frac{4}{x-2}=\frac{x^2-4}{x-2}。對(duì)分子因式分解，\frac{x^2-4}{x-2}=\frac{(x+2)(x-2)}{x-2}=x+2。原式變?yōu)?x+2)\div\frac{x+2}{2x}=(x+2)\times\frac{2x}{x+2}=2x。求值：當(dāng)x=\frac{1}{2}時(shí)，2x=2\times\frac{1}{2}=1?；?jiǎn)：對(duì)分子分母因式分解，\frac{x^2-4x+4}{x^2-4}=\frac{(x-2)^2}{(x+2)(x-2)}=\frac{x-2}{x+2}。原式變?yōu)閈frac{x-2}{x+2}\div\frac{x-2}{x^2+2x}+3=\frac{x-2}{x+2}\times\frac{x(x+2)}{x-2}+3=x+3。由x^2-2x-3=0，因式分解得(x-3)(x+1)=0，解得x=3或x=-1。當(dāng)x=3時(shí)，x+3=3+3=6；當(dāng)x=-1時(shí)，原式有意義，x+3=-1+3=2?；?jiǎn)：對(duì)分子分母因式分解，\frac{m^2-6m+9}{m^2-9}=\frac{(m-3)^2}{(m+3)(m-3)}=\frac{m-3}{m+3}。對(duì)括號(hào)內(nèi)通分：\frac{m-3}{m+3}-\frac{m-9}{m^2+6m+9}=\frac{m-3}{m+3}-\frac{m-9}{(m+3)^2}=\frac{(m-3)(m+3)-(m-9)}{(m+3)^2}=\frac{m^2-9-m+9}{(m+3)^2}=\frac{m^2-m}{(m+3)^2}。原式變?yōu)閈frac{m-3}{m+3}\div\frac{m^2-m}{(m+3)^2}=\frac{m-3}{m+3}\times\frac{(m+3)^2}{m(m-1)}=\frac{(m-3)(m+3)}{m(m-1)}=\frac{m^2-9}{m(m-1)}。求值：當(dāng)m=\sqrt{3}-3時(shí)，代入得\frac{(\sqrt{3}-3)^2-9}{(\sqrt{3}-3)(\sqrt{3}-3-1)}先計(jì)算分子(\sqrt{3}-3)^2-9=3-6\sqrt{3}+9-9=3-6\sqrt{3}。分母(\sqrt{3}-3)(\sqrt{3}-4)=3-4\sqrt{3}-3\sqrt{3}+12=15-7\sqrt{3}。原式=\frac{3-6\sqrt{3}}{15-7\sqrt{3}}=\frac{(3-6\sqrt{3})(15+7\sqrt{3})}{(15-7\sqrt{3})(15+7\sqrt{3})}展開分子45+21\sqrt{3}-90\sqrt{3}-126=-81-69\sqrt{3}。展開分母225-147=78。所以值為\frac{-81-69\sqrt{3}}{78}=-\frac{27+23\sqrt{3}}{26}?；?jiǎn)：對(duì)括號(hào)內(nèi)通分，\frac{1}{x+1}-\frac{1}{x-1}=\frac{x-1-(x+1)}{(x+1)(x-1)}=\frac{x-1-x-1}{(x+1)(x-1)}=\frac{-2}{(x+1)(x-1)}。原式變?yōu)閈frac{-2}{(x+1)(x-1)}\div\frac{2}{1-x}=\frac{-2}{(x+1)(x-1)}\times\frac{1-x}{2}=\frac{1}{x+1}。求值：當(dāng)x=\sqrt{2}-1時(shí)，\frac{1}{x+1}=\frac{1}{\sqrt{2}-1+1}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}?；?jiǎn)：對(duì)分子因式分解，\frac{a^2-b^2}{a^2+ab}=\frac{(a+b)(a-b)}{a(a+b)}=\frac{a-b}{a}。對(duì)括號(hào)內(nèi)通分，a-\frac{2ab-b^2}{a}=\frac{a^2-2ab+b^2}{a}=\frac{(a-b)^2}{a}。原式變?yōu)閈frac{a-b}{a}\div\frac{(a-b)^2}{a}=\frac{a-b}{a}\times\frac{a}{(a-b)^2}=\frac{1}{a-b}。已知a-b=2，所以值為\frac{1}{2}?；?jiǎn)：對(duì)分子分母因式分解，\frac{x^2-2x+1}{x^2-1}=\frac{(x-1)^2}{(x+1)(x-1)}=\frac{x-1}{x+1}。對(duì)括號(hào)內(nèi)通分，\frac{x-1}{x+1}-x+1=\frac{x-1-(x-1)(x+1)}{x+1}=\frac{x-1-(x^2-1)}{x+1}=\frac{x-1-x^2+1}{x+1}=\frac{-x^2+x}{x+1}。原式變?yōu)閈frac{x-1}{x+1}\div\frac{-x^2+x}{x+1}=\frac{x-1}{x+1}\times\frac{x+1}{-x(x-1)}=-\frac{1}{x}。因?yàn)榉帜覆荒転?，所以x\neq-1，x\neq0，x\neq1，當(dāng)x=2時(shí)，-\frac{1}{x}=-\frac{1}{2}?；?jiǎn)：對(duì)分子分母因式分解，\frac{a^2-4}{a^2+6a+9}=\frac{(a+2)(a-2)}{(a+3)^2}，\frac{a-2}{2a+6}=\frac{a-2}{2(a+3)}。原式變?yōu)閈frac{(a+2)(a-2)}{(a+3)^2}\div\frac{a-2}{2(a+3)}-\frac{2}{a+3}=\frac{(a+2)(a-2)}{(a+3)^2}\times\frac{2(a+3)}{a-2}-\frac{2}{a+3}=\frac{2(a+2)}{a+3}-\frac{2}{a+3}=\frac{2a+4-2}{a+3}=\frac{2a+2}{a+3}。計(jì)算a=(\frac{1}{2})^{-2}-3^0=4-1=3。當(dāng)a=3時(shí)，\frac{2a+2}{a+3}=\frac{2\times3+2}{3+3}=\frac{8}{6}=\frac{4}{3}。已知x^2+3x-1=0，兩邊同時(shí)除以x（x\neq0，若x=0，則x^2+3x-1=