分式有意義的題目及答案一、選擇題（共20分）1.下列分式中，有意義的是（）A.\(\frac{1}{x-2}\)當\(x=2\)時B.\(\frac{1}{x+3}\)當\(x=-3\)時C.\(\frac{1}{x-1}\)當\(x=1\)時D.\(\frac{1}{x+1}\)當\(x\)為任意實數(shù)時答案：D2.若分式\(\frac{2}{x-1}\)有意義，則\(x\)的取值范圍是（）A.\(x>1\)B.\(x<1\)C.\(x\neq1\)D.\(x\)為任意實數(shù)答案：C3.分式\(\frac{1}{x+2}\)在\(x\)取何值時分式無意義（）A.\(x=-2\)B.\(x=0\)C.\(x=1\)D.\(x=2\)答案：A4.若分式\(\frac{3x-6}{2x-4}\)有意義，則\(x\)的取值范圍是（）A.\(x\neq2\)B.\(x\neq3\)C.\(x\neq-3\)D.\(x\)為任意實數(shù)答案：A5.分式\(\frac{x-2}{x^2-4}\)在\(x\)取何值時分式無意義（）A.\(x=2\)B.\(x=-2\)C.\(x=0\)D.\(x=1\)答案：A、B二、填空題（共20分）6.分式\(\frac{a}{a-1}\)有意義的條件是\(a\neq\)________。答案：17.分式\(\frac{1}{x-1}\)有意義的條件是\(x\neq\)________。答案：18.分式\(\frac{2}{x+3}\)在\(x=-3\)時分式無意義，因為分母為________。答案：09.分式\(\frac{3}{x^2-4}\)在\(x=\pm2\)時分式無意義，因為分母為________。答案：010.分式\(\frac{5}{x^2+1}\)對于任意實數(shù)\(x\)都有意義，因為分母\(x^2+1\)永遠________。答案：大于0三、計算題（共30分）11.計算分式\(\frac{1}{x-2}+\frac{1}{x+2}\)的值，當\(x=3\)時。答案：\(\frac{1}{3-2}+\frac{1}{3+2}=1+\frac{1}{5}=\frac{6}{5}\)12.計算分式\(\frac{2x}{x^2-4}\)的值，當\(x=5\)時。答案：\(\frac{2\cdot5}{5^2-4}=\frac{10}{25-4}=\frac{10}{21}\)13.計算分式\(\frac{x-1}{x^2-1}\)的值，當\(x=0\)時。答案：\(\frac{0-1}{0^2-1}=\frac{-1}{-1}=1\)14.計算分式\(\frac{3x+6}{x^2-9}\)的值，當\(x=-3\)時。答案：\(\frac{3\cdot(-3)+6}{(-3)^2-9}=\frac{-9+6}{9-9}=\frac{-3}{0}\)（無意義）15.計算分式\(\frac{2x-4}{x^2-4x+4}\)的值，當\(x=2\)時。答案：\(\frac{2\cdot2-4}{2^2-4\cdot2+4}=\frac{4-4}{4-8+4}=\frac{0}{0}\)（無意義）四、化簡題（共30分）16.化簡分式\(\frac{2x}{x^2-4x+4}\)。答案：\(\frac{2x}{(x-2)^2}\)17.化簡分式\(\frac{x^2-9}{x^2-6x+9}\)。答案：\(\frac{(x+3)(x-3)}{(x-3)^2}=\frac{x+3}{x-3}\)（當\(x\neq3\)）18.化簡分式\(\frac{3x-6}{x^2-4}\)。答案：\(\frac{3(x-2)}{(x+2)(x-2)}=\frac{3}{x+2}\)（當\(x\neq2\)）19.化簡分式\(\frac{x^2-4x+4}{x^2-6x+9}\)。答案：\(\frac{(x-2)^2}{(x-3)^2}\)20.化簡分式\(\frac{2x^2-8}{x^2-4x