分式除法的計(jì)算題目及答案

單項(xiàng)選擇題(每題2分,共10題)1.計(jì)算$\frac{2}{x}\div\frac{4}{x^2}$的結(jié)果是(）A.$\frac{1}{2x}$B.$\frac{x}{2}$C.$\frac{2}{x}$D.$\frac{2x}{1}$答案:B解析:$\frac{2}{x}\div\frac{4}{x^2}=\frac{2}{x}\times\frac{x^2}{4}=\frac{2x^2}{4x}=\frac{x}{2}$2.分式$\frac{a}{b^2}\div\frac{2a^2}{b^3}$的結(jié)果是()A.$\frac{2a}$B.$\frac{2a}$C.$\frac{a}{2b}$D.$\frac{2b}{a}$答案:A解析:$\frac{a}{b^2}\div\frac{2a^2}{b^3}=\frac{a}{b^2}\times\frac{b^3}{2a^2}=\frac{ab^3}{2a^2b^2}=\frac{2a}$3.計(jì)算$\frac{x+2}{x-3}\div\frac{x^2+2x}{x^2-6x+9}$的結(jié)果是()A.$\frac{x-3}{x}$B.$\frac{x}{x-3}$C.$\frac{x+3}{x}$D.$\frac{x}{x+3}$答案:A解析:因式分解后$\frac{x+2}{x-3}\times\frac{(x-3)^2}{x(x+2)}=\frac{x-3}{x}$4.分式$\frac{3}{m+2}\div\frac{6}{m^2-4}$的結(jié)果是()A.$\frac{m-2}{2}$B.$\frac{2}{m-2}$C.$\frac{m+2}{2}$D.$\frac{2}{m+2}$答案:A解析：$m^2-4=(m+2)(m-2)$,原式$=\frac{3}{m+2}\times\frac{(m+2)(m-2)}{6}=\frac{m-2}{2}$5.計(jì)算$\frac{2x}{x^2-4}\div\frac{1}{x-2}$的結(jié)果是()A.$\frac{2x}{x+2}$B.$\frac{2x}{x-2}$C.$2x$D.$\frac{2}{x+2}$答案:A解析：$x^2-4=(x+2)(x-2)$,原式$=\frac{2x}{(x+2)(x-2)}\times(x-2)=\frac{2x}{x+2}$6.分式$\frac{a^2-1}{a^2+2a+1}\div\frac{a-1}{a+1}$的結(jié)果是()A.1B.-1C.$a-1$D.$a+1$答案:A解析:因式分解后$\frac{(a+1)(a-1)}{(a+1)^2}\times\frac{a+1}{a-1}=1$7.計(jì)算$\frac{4}{x^2-1}\div\frac{2}{x-1}$的結(jié)果是()A.$\frac{2}{x+1}$B.$\frac{1}{x+1}$C.$\frac{2}{x-1}$D.$\frac{1}{x-1}$答案:A解析：$x^2-1=(x+1)(x-1)$,原式$=\frac{4}{(x+1)(x-1)}\times\frac{x-1}{2}=\frac{2}{x+1}$8.分式$\frac{3y}{2x}\div\frac{6y^2}{x^2}$的結(jié)果是()A.$\frac{x}{4y}$B.$\frac{4y}{x}$C.$\frac{x}{2y}$D.$\frac{2y}{x}$答案:A解析:原式$=\frac{3y}{2x}\times\frac{x^2}{6y^2}=\frac{x}{4y}$9.計(jì)算$\frac{x^2+3x}{x^2-9}\div\frac{x+3}{x-3}$的結(jié)果是()A.1B.-1C.$x$D.$\frac{x}{x+3}$答案:D解析:因式分解后$\frac{x(x+3)}{(x+3)(x-3)}\times\frac{x-3}{x+3}=\frac{x}{x+3}$10.分式$\frac{2}{x-1}\div\frac{4}{x^2-1}$的結(jié)果是()A.$\frac{x+1}{2}$B.$\frac{2}{x+1}$C.$\frac{x-1}{2}$D.$\frac{2}{x-1}$答案:A解析：$x^2-1=(x+1)(x-1)$,原式$=\frac{2}{x-1}\times\frac{(x+1)(x-1)}{4}=\frac{x+1}{2}$多項(xiàng)選擇題(每題2分,共10題)1.下列分式除法運(yùn)算正確的是(）A.$\frac{2}{a}\div\frac{4}{a}=\frac{1}{2}$B.$\frac{a}{b^2}\div\frac{2a^2}{b^3}=\frac{2a}$C.$\frac{x+2}{x-3}\div\frac{x^2+2x}{x^2-6x+9}=\frac{x-3}{x}$D.$\frac{3}{m+2}\div\frac{6}{m^2-4}=\frac{m-2}{2}$答案:ABCD判斷題(每題2分,共10題)1.$\frac{2}{x}\div\frac{4}{x^2}=\frac{x}{2}$(√)2.$\frac{a}{b^2}\div\frac{2a^2}{b^3}=\frac{2a}$(×)3.$\frac{x+2}{x-3}\div\frac{x^2+2x}{x^2-6x+9}=\frac{x-3}{x}$(√)4.$\frac{3}{m+2}\div\frac{6}{m^2-4}=\frac{m-2}{2}$(√)5.$\frac{2x}{x^2-4}\div\frac{1}{x-2}=\frac{2x}{x+2}$(√)6.$\frac{a^2-1}{a^2+2a+1}\div\frac{a-1}{a+1}=1$(√)7.$\frac{4}{x^2-1}\div\frac{2}{x-1}=\frac{2}{x+1}$(√)8.$\frac{3y}{2x}\div\frac{6y^2}{x^2}=\frac{x}{4y}$(√)9.$\frac{x^2+3x}{x^2-9}\div\frac{x+3}{x-3}=x$(×)10.$\frac{2}{x-1}\div\frac{4}{x^2-1}=\frac{x+1}{2}$(√）簡(jiǎn)答題(每題5分,共4題)1.計(jì)算$\frac{5}{x}\div\frac{10}{x^2}$。答案:$\frac{5}{x}\times\frac{x^2}{10}=\frac{x}{2}$2.化簡(jiǎn)$\frac{x^2-4}{x+2}\div\frac{x-2}{x^2-4x+4}$。答案:因式分解后$\frac{(x+2)(x-2)}{x+2}\times\frac{(x-2)^2}{x-2}=(x-2)^2$3.計(jì)算$\frac{3a}{b^2}\div\frac{6a^2}{b^3}$。答案:$\frac{3a}{b^2}\times\frac{b^3}{6a^2}=\frac{2a}$4.化簡(jiǎn)$\frac{x^2+5x}{x^2-25}\div\frac{x+5}{x-5}$。答案:因式分解后$\frac{x(x+5)}{(x+5)(x-5)}\times\frac{x-5}{x+5}=\frac{x}{x+5}$討論題(每題5分,共4題)1.分式除法運(yùn)算中需要注意什么?答案：轉(zhuǎn)化為乘法,注意因式分解和約分,保證分母不為零。2.比較分式$\frac{2}{x}\div\frac{4}{x^2}$與$\frac{4}{x^2}\div\frac{2}{x}$的結(jié)果有何不同。答案:$\frac{2}{x}\div\frac{4}{x^2}=\frac{x}{2}$,$\frac{4}{x^2}\