高中通分的題目及答案

一、單項(xiàng)選擇題1.把\(\frac{1}{2x}\)，\(\frac{1}{3y}\)通分后分別是（）A.\(\frac{3y}{6xy}\)，\(\frac{2x}{6xy}\)B.\(\frac{2x}{6xy}\)，\(\frac{3y}{6xy}\)C.\(\frac{3y}{3xy}\)，\(\frac{2x}{3xy}\)D.\(\frac{y}{2xy}\)，\(\frac{x}{3xy}\)答案：A2.分式\(\frac{1}{x^2-4}\)與\(\frac{1}{x-2}\)通分后，\(\frac{1}{x-2}\)變?yōu)椋ǎ〢.\(\frac{x+2}{(x+2)(x-2)}\)B.\(\frac{x-2}{(x+2)(x-2)}\)C.\(\frac{1}{x^2-4}\)D.\(\frac{x+2}{x^2-2}\)答案：A3.分式\(\frac{1}{a^2-ab}\)與\(\frac{1}{a^2-b^2}\)的最簡(jiǎn)公分母是（）A.\(a(a-b)(a+b)\)B.\(a(a-b)\)C.\((a^2-ab)(a^2-b^2)\)D.\((a-b)^2(a+b)\)答案：A4.將\(\frac{2}{3a^2}\)，\(\frac{1}{6ab^2}\)通分，正確的是（）A.\(\frac{4b^2}{6a^2b^2}\)，\(\frac{a}{6a^2b^2}\)B.\(\frac{4b^2}{6a^2b^2}\)，\(\frac{1}{6a^2b^2}\)C.\(\frac{2}{6a^2b^2}\)，\(\frac{1}{6a^2b^2}\)D.\(\frac{4b^2}{3a^2b^2}\)，\(\frac{a}{3a^2b^2}\)答案：A5.把\(\frac{3}{x-1}\)，\(\frac{2}{x+1}\)通分，結(jié)果是（）A.\(\frac{3(x+1)}{(x-1)(x+1)}\)，\(\frac{2(x-1)}{(x-1)(x+1)}\)B.\(\frac{3(x-1)}{(x-1)(x+1)}\)，\(\frac{2(x+1)}{(x-1)(x+1)}\)C.\(\frac{3}{(x-1)(x+1)}\)，\(\frac{2}{(x-1)(x+1)}\)D.\(\frac{3(x+1)}{(x+1)^2}\)，\(\frac{2(x-1)}{(x-1)^2}\)答案：A6.分式\(\frac{1}{x^2+2x+1}\)與\(\frac{1}{x^2-1}\)的最簡(jiǎn)公分母是（）A.\((x+1)^2(x-1)\)B.\((x+1)(x-1)\)C.\((x^2+2x+1)(x^2-1)\)D.\((x+1)^2\)答案：A7.把\(\frac{1}{x^2-3x}\)，\(\frac{1}{x^2-9}\)通分后，\(\frac{1}{x^2-9}\)變?yōu)椋ǎ〢.\(\frac{x}{x(x+3)(x-3)}\)B.\(\frac{x}{(x+3)(x-3)}\)C.\(\frac{1}{x(x+3)(x-3)}\)D.\(\frac{x-3}{x(x+3)(x-3)}\)答案：A8.分式\(\frac{2}{x^2-4x+4}\)與\(\frac{1}{x^2-4}\)通分后，\(\frac{2}{x^2-4x+4}\)變?yōu)椋ǎ〢.\(\frac{2(x+2)}{(x-2)^2(x+2)}\)B.\(\frac{2(x-2)}{(x-2)^2(x+2)}\)C.\(\frac{2}{(x-2)^2(x+2)}\)D.\(\frac{2}{(x-2)(x+2)}\)答案：A9.把\(\frac{3}{2a^2b}\)，\(\frac{1}{3ab^2}\)通分，最簡(jiǎn)公分母是（）A.\(6a^2b^2\)B.\(6ab\)C.\(5a^2b^2\)D.\(6a^3b^3\)答案：A10.分式\(\frac{1}{x^2-5x+6}\)與\(\frac{1}{x^2-4}\)通分后，\(\frac{1}{x^2-4}\)變?yōu)椋ǎ〢.\(\frac{x-3}{(x-2)(x+2)(x-3)}\)B.\(\frac{x+3}{(x-2)(x+2)(x-3)}\)C.\(\frac{1}{(x-2)(x+2)(x-3)}\)D.\(\frac{x-2}{(x-2)(x+2)(x-3)}\)答案：A二、多項(xiàng)選擇題1.以下關(guān)于通分的說(shuō)法正確的是（）A.通分的依據(jù)是分式的基本性質(zhì)B.通分是把幾個(gè)異分母分式化為與原來(lái)分式相等的同分母分式C.通分后分式的值不變D.通分的關(guān)鍵是確定最簡(jiǎn)公分母答案：ABCD2.對(duì)于分式\(\frac{1}{x^2-1}\)和\(\frac{1}{x+1}\)，以下說(shuō)法正確的是（）A.最簡(jiǎn)公分母是\(x^2-1\)B.通分后\(\frac{1}{x+1}=\frac{x-1}{x^2-1}\)C.通分后\(\frac{1}{x^2-1}\)不變D.它們可以通分答案：ABCD3.下列分式中，最簡(jiǎn)公分母是\(6x^2y^3\)的有（）A.\(\frac{1}{2x^2y}\)，\(\frac{1}{3y^3}\)B.\(\frac{1}{3x^2y^2}\)，\(\frac{1}{2xy^3}\)C.\(\frac{1}{6x^2y^3}\)，\(\frac{1}{xy}\)D.\(\frac{1}{x^2y}\)，\(\frac{1}{6y^3}\)答案：AB4.把\(\frac{3}{x^2-2x}\)，\(\frac{2}{x^2-4}\)通分，下列說(shuō)法正確的是（）A.先對(duì)分母因式分解，\(x^2-2x=x(x-2)\)，\(x^2-4=(x+2)(x-2)\)B.最簡(jiǎn)公分母是\(x(x+2)(x-2)\)C.\(\frac{3}{x^2-2x}=\frac{3(x+2)}{x(x+2)(x-2)}\)D.\(\frac{2}{x^2-4}=\frac{2x}{x(x+2)(x-2)}\)答案：ABCD5.關(guān)于分式通分，以下哪些是確定最簡(jiǎn)公分母的正確方法（）A.取各分母系數(shù)的最小公倍數(shù)作為最簡(jiǎn)公分母的系數(shù)B.凡單獨(dú)出現(xiàn)的字母，連同它的指數(shù)作為最簡(jiǎn)公分母的一個(gè)因式C.同底數(shù)冪取次數(shù)最高的作為最簡(jiǎn)公分母的一個(gè)因式D.最簡(jiǎn)公分母是所有分母的乘積答案：ABC6.分式\(\frac{1}{a^2-4a+4}\)與\(\frac{1}{a^2-4}\)通分過(guò)程中，正確的有（）A.對(duì)\(a^2-4a+4=(a-2)^2\)，\(a^2-4=(a+2)(a-2)\)因式分解B.最簡(jiǎn)公分母是\((a-2)^2(a+2)\)C.\(\frac{1}{a^2-4a+4}=\frac{a+2}{(a-2)^2(a+2)}\)D.\(\frac{1}{a^2-4}=\frac{a-2}{(a-2)^2(a+2)}\)答案：ABCD7.下列分式組中，最簡(jiǎn)公分母相同的是（）A.\(\frac{1}{x^2-9}\)，\(\frac{1}{x^2+6x+9}\)B.\(\frac{1}{x^2-1}\)，\(\frac{1}{x^2-2x+1}\)C.\(\frac{1}{x^2-4x+4}\)，\(\frac{1}{x^2-4}\)D.\(\frac{1}{x^2+2x}\)，\(\frac{1}{x^2-2x}\)答案：AB8.通分\(\frac{2}{3x^2y}\)，\(\frac{3}{4xy^2}\)時(shí)，下列步驟正確的是（）A.先確定最簡(jiǎn)公分母為\(12x^2y^2\)B.\(\frac{2}{3x^2y}=\frac{2\times4y}{3x^2y\times4y}=\frac{8y}{12x^2y^2}\)C.\(\frac{3}{4xy^2}=\frac{3\times3x}{4xy^2\times3x}=\frac{9x}{12x^2y^2}\)D.通分后的兩個(gè)分式分母相同答案：ABCD9.對(duì)于分式\(\frac{1}{x^2+3x+2}\)和\(\frac{1}{x^2+2x+1}\)，說(shuō)法正確的是（）A.對(duì)分母因式分解，\(x^2+3x+2=(x+1)(x+2)\)，\(x^2+2x+1=(x+1)^2\)B.最簡(jiǎn)公分母是\((x+1)^2(x+2)\)C.\(\frac{1}{x^2+3x+2}=\frac{x+1}{(x+1)^2(x+2)}\)D.\(\frac{1}{x^2+2x+1}=\frac{x+2}{(x+1)^2(x+2)}\)答案：ABCD10.以下關(guān)于分式通分與約分的關(guān)系，說(shuō)法正確的是（）A.通分是把異分母化為同分母，約分是把分子分母的公因式約去B.通分和約分都是依據(jù)分式的基本性質(zhì)C.通分是擴(kuò)大分式的值，約分是縮小分式的值D.通分和約分都不改變分式的值答案：ABD三、判斷題1.通分就是把分母不同的分?jǐn)?shù)化為分母相同的分?jǐn)?shù)。（√）2.分式通分后，分式的值可能會(huì)改變。（×）3.最簡(jiǎn)公分母是所有分母的乘積。（×）4.把\(\frac{1}{x-1}\)和\(\frac{1}{x+1}\)通分，最簡(jiǎn)公分母是\(x^2-1\)。（√）5.通分\(\frac{1}{2x}\)和\(\frac{1}{3x}\)，最簡(jiǎn)公分母是\(6x\)。（√）6.分式\(\frac{1}{x^2-4}\)和\(\frac{1}{x^2+4x+4}\)的最簡(jiǎn)公分母是\((x+2)^2(x-2)\)。（√）7.通分的關(guān)鍵是找到所有分母的最大公因數(shù)。（×）8.把\(\frac{2}{3a}\)和\(\frac{3}{4a^2}\)通分后，\(\frac{2}{3a}=\frac{8a}{12a^2}\)。（√）9.對(duì)于分式\(\frac{1}{x^2-3x}\)和\(\frac{1}{x^2-9}\)，通分后\(\frac{1}{x^2-9}=\frac{x}{x(x+3)(x-3)}\)。（√）10.兩個(gè)分式通分后，分母一定相同。（√）四、簡(jiǎn)答題1.簡(jiǎn)述通分的步驟。通分首先要對(duì)各分式的分母進(jìn)行因式分解，找出最簡(jiǎn)公分母。確定最簡(jiǎn)公分母的方法是：取各分母系數(shù)的最小公倍數(shù)，凡單獨(dú)出現(xiàn)的字母連同它的指數(shù)作為最簡(jiǎn)公分母的一個(gè)因式，同底數(shù)冪取次數(shù)最高的。然后根據(jù)分式的基本性質(zhì)，將各分式的分子分母同乘適當(dāng)?shù)恼?，使各分式化為分母相同的分式?.如何確定多個(gè)分式的最簡(jiǎn)公分母？確定多個(gè)分式最簡(jiǎn)公分母，先分別對(duì)各分母進(jìn)行因式分解。系數(shù)取各分母系數(shù)的最小公倍數(shù)，單獨(dú)出現(xiàn)的字母及其指數(shù)都作為最簡(jiǎn)公分母的因式，對(duì)于相同底數(shù)的冪，取次數(shù)最高的作為最簡(jiǎn)公分母的因式。將這些因式相乘，得到的結(jié)果就是最簡(jiǎn)公分母。3.通分\(\frac{1}{x^2-1}\)與\(\frac{1}{x^2+2x+1}\)。先對(duì)分母因式分解，\(x^2-1=(x+1)(x-1)\)，\(x^2+2x+1=(x+1)^2\)。最簡(jiǎn)公分母是\((x+1)^2(x-1)\)。\(\frac{1}{x^2-1}=\frac{x+1}{(x+1)^2(x-1)}\)，\(\frac{1}{x^2+2x+1}=\frac{x-1}{(x+1)^2(x-1)}\)。4.說(shuō)明通分\(\frac{3}{2x^2y}\)與\(\frac{5}{3xy^2}\)的過(guò)程。先確定最簡(jiǎn)公分母，系數(shù)\(2\)和\(3\)的最小公倍數(shù)是\(6\)，\(x\)的最高次冪是\(x^2\)，\(y\)的最高次冪是\(y^2\)，所以最簡(jiǎn)公分母是\(6x^2y^2\)。\(\frac{3}{2x^2y}=\frac{3\times3