初中分式培優(yōu)題目及答案

一、單項(xiàng)選擇題（每題2分，共10題）1.下列分式中，當(dāng)x=2時(shí)，分式的值為0的是（）A.\(\frac{x-2}{x+1}\)B.\(\frac{x^2-4}{x-2}\)C.\(\frac{x+2}{x-2}\)D.\(\frac{x^2-2x}{x-2}\)答案：B2.分式\(\frac{3x-6}{x^2-4}\)約分后等于（）A.\(\frac{3}{x-2}\)B.\(\frac{3}{x+2}\)C.\(\frac{1}{x-2}\)D.\(\frac{1}{x+2}\)答案：A3.分式\(\frac{2x+6}{x^2+5x+6}\)的值為1，則x的值為（）A.-2B.-3C.1D.2答案：D4.若分式\(\frac{x-1}{x^2-1}\)的值為0，則x的值為（）A.1B.-1C.0D.2答案：A5.分式\(\frac{a^2-4}{a^2+2a-8}\)的值為0，則a的值為（）A.-2B.2C.-4D.4答案：B6.分式\(\frac{x^2-9}{x^2+6x+9}\)約分后等于（）A.\(\frac{x-3}{x+3}\)B.\(\frac{x+3}{x-3}\)C.\(\frac{x-3}{x-3}\)D.\(\frac{x+3}{x+3}\)答案：A7.分式\(\frac{2x^2-8}{x^2-4}\)約分后等于（）A.\(\frac{2x-4}{x-2}\)B.\(\frac{2x+4}{x+2}\)C.\(\frac{2}{x-2}\)D.\(\frac{2}{x+2}\)答案：C8.分式\(\frac{x^2-1}{x^2+2x+1}\)約分后等于（）A.\(\frac{x-1}{x+1}\)B.\(\frac{x+1}{x-1}\)C.\(\frac{x-1}{x-1}\)D.\(\frac{x+1}{x+1}\)答案：A9.分式\(\frac{3x^2-12}{x^2-4}\)約分后等于（）A.\(\frac{3x-6}{x-2}\)B.\(\frac{3x+6}{x+2}\)C.\(\frac{3}{x-2}\)D.\(\frac{3}{x+2}\)答案：A10.分式\(\frac{2x^2-6x}{x^2-9}\)約分后等于（）A.\(\frac{2x-6}{x-3}\)B.\(\frac{2x+6}{x+3}\)C.\(\frac{2}{x-3}\)D.\(\frac{2}{x+3}\)答案：C二、多項(xiàng)選擇題（每題2分，共10題）1.下列分式中，當(dāng)x=1時(shí)，分式的值為0的是（）A.\(\frac{x-1}{x+1}\)B.\(\frac{x^2-1}{x-1}\)C.\(\frac{x+1}{x-1}\)D.\(\frac{x^2-1}{x+1}\)答案：B,D2.分式\(\frac{2x-4}{x^2-4}\)約分后等于（）A.\(\frac{2}{x-2}\)B.\(\frac{2}{x+2}\)C.\(\frac{1}{x-2}\)D.\(\frac{1}{x+2}\)答案：A3.分式\(\frac{3x-9}{x^2-9}\)約分后等于（）A.\(\frac{3}{x-3}\)B.\(\frac{3}{x+3}\)C.\(\frac{1}{x-3}\)D.\(\frac{1}{x+3}\)答案：A4.若分式\(\frac{x-2}{x^2-4}\)的值為1，則x的值為（）A.2B.-2C.3D.-3答案：C5.分式\(\frac{2x^2-8}{x^2-4}\)約分后等于（）A.\(\frac{2x-4}{x-2}\)B.\(\frac{2x+4}{x+2}\)C.\(\frac{2}{x-2}\)D.\(\frac{2}{x+2}\)答案：C6.分式\(\frac{x^2-1}{x^2+2x+1}\)約分后等于（）A.\(\frac{x-1}{x+1}\)B.\(\frac{x+1}{x-1}\)C.\(\frac{x-1}{x-1}\)D.\(\frac{x+1}{x+1}\)答案：A7.分式\(\frac{3x^2-12}{x^2-4}\)約分后等于（）A.\(\frac{3x-6}{x-2}\)B.\(\frac{3x+6}{x+2}\)C.\(\frac{3}{x-2}\)D.\(\frac{3}{x+2}\)答案：A8.分式\(\frac{2x^2-6x}{x^2-9}\)約分后等于（）A.\(\frac{2x-6}{x-3}\)B.\(\frac{2x+6}{x+3}\)C.\(\frac{2}{x-3}\)D.\(\frac{2}{x+3}\)答案：C9.分式\(\frac{2x-4}{x^2-4}\)約分后等于（）A.\(\frac{2}{x-2}\)B.\(\frac{2}{x+2}\)C.\(\frac{1}{x-2}\)D.\(\frac{1}{x+2}\)答案：A10.分式\(\frac{3x-9}{x^2-9}\)約分后等于（）A.\(\frac{3}{x-3}\)B.\(\frac{3}{x+3}\)C.\(\frac{1}{x-3}\)D.\(\frac{1}{x+3}\)答案：A三、判斷題（每題2分，共10題）1.分式\(\frac{x^2-1}{x^2+1}\)的值為0，則x=1。（）答案：正確2.分式\(\frac{2x-4}{x^2-4}\)約分后等于\(\frac{2}{x-2}\)。（）答案：正確3.分式\(\frac{3x-9}{x^2-9}\)約分后等于\(\frac{3}{x-3}\)。（）答案：正確4.分式\(\frac{x^2-1}{x^2+2x+1}\)約分后等于\(\frac{x-1}{x+1}\)。（）答案：正確5.分式\(\frac{2x^2-8}{x^2-4}\)約分后等于\(\frac{2}{x-2}\)。（）答案：正確6.分式\(\frac{3x^2-12}{x^2-4}\)約分后等于\(\frac{3}{x-2}\)。（）答案：正確7.分式\(\frac{2x^2-6x}{x^2-9}\)約分后等于\(\frac{2}{x-3}\)。（）答案：正確8.分式\(\frac{2x-4}{x^2-4}\)約分后等于\(\frac{2}{x+2}\)。（）答案：錯(cuò)誤9.分式\(\frac{3x-9}{x^2-9}\)約分后等于\(\frac{3}{x+3}\)。（）答案：錯(cuò)誤10.分式\(\frac{x^2-1}{x^2+2x+1}\)約分后等于\(\frac{x+1}{x-1}\)。（）答案：錯(cuò)誤四、簡(jiǎn)答題（每題5分，共4題）1.分式\(\frac{x^2-4}{x^2-5x+6}\)約分后等于多少？答案：分式\(\frac{x^2-4}{x^2-5x+6}\)約分后等于\(\frac{x-2}{x-3}\)。2.分式\(\frac{2x^2-8}{x^2-4}\)的值為1，求x的值。答案：分式\(\frac{2x^2-8}{x^2-4}\)的值為1，即\(\frac{2(x^2-4)}{x^2-4}=1\)，解得x=±2。3.分式\(\frac{3x-6}{x^2-4}\)約分后等于\(\frac{3}{x+2}\)，求x的值。答案：分式\(\frac{3x-6}{x^2-4}\)約分后等于\(\frac{3}{x+2}\)，即\(\frac{3(x-2)}{(x+2)(x-2)}=\frac{3}{x+2}\)，解得x=0。4.分式\(\frac{x^2-1}{x^2+2x+1}\)的值為0，求x的值。答案：分式\(\frac{x^2-1}{x^2+2x+1}\)的值為0，即\(\frac{(x-1)(x+1)}{(x+1)^2}=0\)，解得x=-1。五、討論題（每題5分，共4題）1.分式\(\frac{x^2-4}{x^2-5x+6}\)約分后等于多少？并討論其值的變化情況。答案：分式\(\frac{x^2-4}{x^2-5x+6}\)約分后等于\(\frac{x-2}{x-3}\)。當(dāng)x=2時(shí)，分式值為0；當(dāng)x=3時(shí)，分式無意義；當(dāng)x>3時(shí)，分式值為正；當(dāng)x<2時(shí)，分式值為負(fù)。2.分式\(\frac{2x^2-8}{x^2-4}\)的值為1，求x的值，并討論其解的合理性。答案：分式\(\frac{2x^2-8}{x^2-4}\)的值為1，即\(\frac{2(x^2-4)}{x^2-4}=1\)，解得x=±2。當(dāng)x=±2時(shí)，分母為0，分式無意義，故解不合理。3.分式\(\frac{3x-6}{x^2-4}\)約分后等于\(\frac{3}{x+2}\)，求x的值，并討論其解的合理性。答案：分式\(\frac{3x-6}{x^2-4}\)約分后等于\(\frac{3}{x+2}\)，即\(\frac{3