數(shù)學(xué)分式重難題目及答案一、選擇題（每題3分，共15分）1.若分式\(\frac{a}\)的值為零，則以下哪個條件必須成立？A.\(a=0\)且\(b\neq0\)B.\(a=0\)或\(b=0\)C.\(a=0\)且\(b=0\)D.\(a\neq0\)且\(b=0\)答案：A2.分式\(\frac{2x-1}{x^2-1}\)的最簡形式是什么？A.\(\frac{2x-1}{(x-1)(x+1)}\)B.\(\frac{1}{x+1}\)C.\(\frac{1}{x-1}\)D.\(\frac{2}{x}\)答案：C3.若\(\frac{1}{x}=\frac{2}{x+1}\)，則\(x\)的值是多少？A.\(-1\)B.\(1\)C.\(2\)D.\(0\)答案：A4.以下哪個分式在\(x=1\)時無定義？A.\(\frac{1}{x-1}\)B.\(\frac{1}{x+1}\)C.\(\frac{1}{x^2-1}\)D.\(\frac{1}{x^2+1}\)答案：A5.若\(\frac{a}=\frac{c}21k11ho\)，則\(ad=bc\)是否成立？A.總是成立B.從不成立C.僅當(dāng)\(a\)和\(d\)都不為零時成立D.僅當(dāng)\(b\)和\(c\)都不為零時成立答案：A二、填空題（每題4分，共20分）6.若\(\frac{3}{x-2}=\frac{6}{x+2}\)，則\(x\)的值為_________。答案：47.將分式\(\frac{5x^2-10x}{x^2-4}\)化簡，得到的結(jié)果為_________。答案：\(5x\)8.若\(\frac{a}=\frac{c}0q3sqsa\)且\(a\)、\(b\)、\(c\)、\(d\)均不為零，則\(\frac{a+c}{b+d}=\frac{a}\)是否成立？若成立，\(\frac{a+c}{b+d}\)的值為_________。答案：\(\frac{c}ug913md\)9.若\(\frac{1}{x-1}-\frac{1}{x+1}=\frac{2}{x^2-1}\)，則\(x\)的值為_________。答案：±210.將分式\(\frac{2x^2-8x+8}{x^2-4x+4}\)化簡，得到的結(jié)果為_________。答案：\(2x-4\)三、解答題（每題10分，共40分）11.已知\(\frac{a}=\frac{c}1gxvldl\)，求證\(\frac{a+c}{b+d}=\frac{a}\)。證明：由\(\frac{a}=\frac{c}griz2jq\)，得\(ad=bc\)。\(\frac{a+c}{b+d}=\frac{a\cdotd+c\cdotd}{b\cdotd+d\cdotd}=\frac{ad+bc}{bd+d^2}=\frac{2ad}{bd+d^2}=\frac{ad}{bd}=\frac{a}\)。故\(\frac{a+c}{b+d}=\frac{a}\)成立。12.已知\(\frac{3}{x-2}=\frac{6}{x+2}\)，求\(x\)的值。解：\(3(x+2)=6(x-2)\)，\(3x+6=6x-12\)，\(3x=18\)，\(x=6\)。13.化簡分式\(\frac{2x^3-8x^2+8x}{x^2-4x+4}\)。解：\(\frac{2x^3-8x^2+8x}{x^2-4x+4}=\frac{2x(x^2-4x+4)}{x^2-4x+4}=2x\)。14.解分式方程\(\frac{1}{x-1}-\frac{1}{x+1}=\frac{2}{x^2-1}\)。解：\(\frac{(x+1)-(x-1)}{(x-1)(x+1)}=\frac{2}{x^2-1}\)，\(\frac{2}{x^2-1}=\frac{2}{x^2-1}\)，\(x^2-1\neq0\)，\(x\neq\pm1\)。四、綜合題（每題10分，共15分）15.已知\(\frac{a}=\frac{c}vs1enn2\)，求\(\frac{a+c}{b+d}\)、\(\frac{a-c}{b-d}\)和\(\frac{ac}{bd}\)的值。解：由\(\frac{a}=\frac{c}bpxp1sx\)，得\(ad=bc\)。\(\frac{a+c}{b+d}=\frac{a\cdotd+c\cdotd}{b\cdotd+d\cdotd}=\frac{ad+bc}{bd+d^2}=\frac{2ad}{bd+d^2}=\frac{ad}{bd}=\frac{a}\)。\(\frac{a-c}{b-d}=\frac{a\cdotd-c\cdotd}{b\cdotd-d\cdotd}=\frac{ad-bc}{bd-d^2}=\frac{ad-bc}{bd-d^2}=\frac{ad}{bd}=\frac{a}\)。\(\frac{ac}{bd}=\frac{a\cdotc}{b\cdotd}=\frac{a}\cdot\frac{c}remuu1l=\frac{a}\cdot\frac{a}{b