分式的計(jì)算題目及答案一、選擇題（每題3分，共15分）1.下列分式中，哪一個(gè)是假分式？A.\(\frac{3}{2}\)B.\(\frac{2}{3}\)C.\(\frac{5}{3}\)D.\(\frac{1}{4}\)答案：C2.計(jì)算分式\(\frac{2x}{3}+\frac{4x}{5}\)的結(jié)果為：A.\(\frac{22x}{15}\)B.\(\frac{14x}{15}\)C.\(\frac{10x}{3}\)D.\(\frac{8x}{15}\)答案：A3.將分式\(\frac{3}{x-2}\)與\(\frac{2}{x+2}\)相乘，結(jié)果為：A.\(\frac{6}{x^2-4}\)B.\(\frac{6}{x^2+4}\)C.\(\frac{6x}{x^2-4}\)D.\(\frac{3x}{x^2-4}\)答案：A4.計(jì)算分式\(\frac{5}{x}-\frac{3}{x+1}\)的結(jié)果為：A.\(\frac{2}{x(x+1)}\)B.\(\frac{2}{x-1}\)C.\(\frac{2x+5}{x(x+1)}\)D.\(\frac{5x-3}{x(x+1)}\)答案：A5.將分式\(\frac{a}\)除以\(\frac{c}z3jilz61osys\)，結(jié)果為：A.\(\frac{ad}{bc}\)B.\(\frac{ac}{bd}\)C.\(\frac{bc}{ad}\)D.\(\frac{bd}{ac}\)答案：A二、填空題（每題4分，共20分）1.計(jì)算分式\(\frac{4}{3}\times\frac{9}{8}\)的結(jié)果為\(\boxed{\frac{3}{2}}\)。2.計(jì)算分式\(\frac{2}{x}+\frac{3}{x-1}\)的結(jié)果為\(\boxed{\frac{5x-3}{x(x-1)}}\)。3.計(jì)算分式\(\frac{5}{x+2}-\frac{3}{x-2}\)的結(jié)果為\(\boxed{\frac{8}{x^2-4}}\)。4.計(jì)算分式\(\frac{a^2}\div\frac{a}{b^2}\)的結(jié)果為\(\boxed{ab}\)。5.計(jì)算分式\(\frac{3x}{x-2}\times\frac{x+2}{5}\)的結(jié)果為\(\boxed{\frac{3x(x+2)}{5(x-2)}}\)。三、計(jì)算題（每題10分，共30分）1.計(jì)算分式\(\frac{2x+3}{x-1}\div\frac{x+1}{x^2-1}\)的結(jié)果。解：\(\frac{2x+3}{x-1}\div\frac{x+1}{x^2-1}=\frac{2x+3}{x-1}\times\frac{(x+1)(x-1)}{x+1}=\frac{2x+3}{1}=2x+3\)答案：\(\boxed{2x+3}\)2.計(jì)算分式\(\frac{3}{x-2}+\frac{4}{x+2}-\frac{7}{x^2-4}\)的結(jié)果。解：\(\frac{3}{x-2}+\frac{4}{x+2}-\frac{7}{x^2-4}=\frac{3(x+2)+4(x-2)-7}{(x-2)(x+2)}=\frac{3x+6+4x-8-7}{x^2-4}=\frac{7x-9}{x^2-4}\)答案：\(\boxed{\frac{7x-9}{x^2-4}}\)3.計(jì)算分式\(\frac{a^2-4}{a+2}\times\frac{a-2}{a^2+2a}\)的結(jié)果。解：\(\frac{a^2-4}{a+2}\times\frac{a-2}{a^2+2a}=\frac{(a+2)(a-2)}{a+2}\times\frac{a-2}{a(a+2)}=\frac{(a-2)^2}{a(a+2)}\)答案：\(\boxed{\frac{(a-2)^2}{a(a+2)}}\)四、綜合題（每題15分，共30分）1.已知\(x=\frac{3}{2}\)，計(jì)算分式\(\frac{1}{x-1}-\frac{1}{x+1}+\frac{2x}{x^2-1}\)的值。解：將\(x=\frac{3}{2}\)代入分式中，得\(\frac{1}{\frac{3}{2}-1}-\frac{1}{\frac{3}{2}+1}+\frac{2\times\frac{3}{2}}{\left(\frac{3}{2}\right)^2-1}=\frac{1}{\frac{1}{2}}-\frac{1}{\frac{5}{2}}+\frac{3}{\frac{9}{4}-1}=2-\frac{2}{5}+\frac{3}{\frac{5}{4}}=2-\frac{2}{5}+\frac{12}{5}=2+\frac{10}{5}=4\)答案：\(\boxed{4}\)2.計(jì)算分式\(\frac{a^2-9}{a^2-4}\div\frac{a+3}{a-3}\times\frac{a+1}{a^2-1}\)的結(jié)果，并化簡。解：\(\frac{a^2-9}{a^2-4}\div\frac{a+3}{a-3}\times\frac{a+1}{a^2-1}=\frac{(a+3)(a-3)}{(a+2)(a-2)}\times\frac{a-3}{a+3}\times\frac{a+1}{