Math topic中文

Fractional to linear

solving simple fractional equations that can be reduced to linear equations such as: x3+x−24=3\dfrac{x}{3} + \dfrac{x - 2}{4} = 3; 3x−2=6\quad \dfrac{3}{x - 2} = 6

Practice questions

  1. 1若关于xx的分式方程4x−2−a2−x=2\dfrac{4}{x-2}-\dfrac{a}{2-x}=2的解为正整数，且关于yy的不等式组{y−22+5<2yy−a⩽0\begin{cases}{\dfrac{y-2}{2}+5< 2y}\\ {y-a\leqslant 0}\end{cases}…
  2. 2分式方程13x−6=34x−8 \dfrac {1}{3x-6} = \dfrac {3}{4x-8}的解的情况为___．
  3. 3分式方程2x+1x−1=3\dfrac{2x+1}{x-1}=3的解是()() A. x=−45x=-\dfrac{4}{5} B. x=45x=\dfrac{4}{5} C. x=−4x=-4 D. x=−4x=-4
  4. 4张明3h3h清点完一批图书的一半，李强加入清点另一半图书的工作，两人合作1.2h1.2h清点完另一半图书.哪个人清点速度快？
  5. 5解下列方程 (1)6x−2=1x+3(1) \dfrac {6}{x-2}= \dfrac {1}{x+3}； (2)x+1x−1−4x2−1=1(2) \dfrac {x+1}{x-1}- \dfrac {4}{x^{2}-1}=1．
  6. 6关于xx的分式方程xx−1−2=k1−x\dfrac{x}{x-1}-2=\dfrac{k}{1-x}的增根为()(\quad) A. x=−1x=-1 B. x=0x=0 C. x=−2x=-2 D. x=1x=1
  7. 7我市某校为了创建书香校园，去年购进一批图书.经了解，科普书的单价比文学书的单价多44元，用1200012000元购进的科普书与用80008000元购进的文学书本数相等． (1)文学书和科普书的单价各多少钱？ (2)今年文学书和科普书的单…
  8. 8Solve x/5+(2x−3)/4=−6x/5 + (2x-3)/4 = -6. Answer x = ... Simplify 2(p−3q)/(10r)+(3q−p)2/r2(p-3q)/(10r) + (3q-p)^2/r. Answer ... Solve the inequality x+1≤7x−24<5x+195x+1 \le \dfrac{7x-2}{4} < \dfrac{5x+19}{5}…
  9. 9T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}} Rearrange the formula to make g the subject. Answer g = ...
  10. 10已知方程21+x−k1−x=6x2−1\dfrac{2}{1+x}-\dfrac{k}{1-x}=\dfrac{6}{x^{2}-1}有增根x=1x=1，求kk的值．
  11. 11(1)解方程：13x−4−10x−3=4x−5−1x−1(2) \dfrac{13}{x-4}- \dfrac{10}{x-3}= \dfrac{4}{x-5}- \dfrac{1}{x-1} (2)已知a2+4a+1=0a^{2}+4a+1=0，且，a4+ma2+13a2+ma2+3a=5\dfrac{{a}^{4}+m{a}^{2}+1}{3{a}^{2}+m{a}^{2}+3a}=5…
  12. 12为了估算湖里有多少条鱼，从湖里捕上100100条做上标记，然后放回湖里，经过一段时间待标记的鱼全混合于鱼群中后，第二次捕得200200条，发现其中带标记的鱼2525条，我们可以估算湖里有鱼 ___ 条.
  13. 13A sheet of rectangular paper has length ll cm and breadth bb cm. If identical squares of side 3 cm are to be cut out f…
  14. 14若1−∣x∣x2−2x+1=0\dfrac{1-\left|x\right|}{{x}^{2}-2x+1} =0， 求1x2017−1\dfrac{1}{{x}^{2017}-1} 的值．
  15. 15若方程5x−2=ax+4x(x−2)\dfrac{5}{x-2}=\dfrac{a}{x}+\dfrac{4}{x(x-2)}有增根，则增根可能为()(\quad) A. 00 B. 22 C. 00或22 D. 11
  16. 16解方程： (1)xx−2−8x2−4=1(2)2x2−4x+1=0(1) \dfrac {x}{x-2}- \dfrac {8}{x^{2}-4}=1(2)2x^{2}-4x+1=0．
  17. 17当x=x= 时，分式1x−1\dfrac{1}{x-1}的值为11．
  18. 18Solve the equation x3−3x−74=8\frac{x}{3} - \frac{3x-7}{4} = 8
  19. 19Factorise completely m2−2mn+n2−p2m^2 - 2mn + n^2 - p^2. Answer ... Express as a single fraction in its simplest form 72x−3+x+16−4x\dfrac{7}{2x-3} + \dfrac{x+1}{6-4x}…
  20. 20一个数的平方是它的相反数，这个数为 ；一个数的立方是它的倒数，这个数是 ．
  21. 21只有颜色不同的1515个红球和若干个白球装在不透明的袋子里，从袋子里摸出一个球记录下颜色后放回，经过多次重复试验，发现摸到红球的频率稳定在0.60.6，则袋中红球与白球共有()(\quad) A. 1010个 B. 1616…
  22. 22若关于xx的分式方程x−ax−1−ax+1=1\dfrac{x-a}{x-1}-\dfrac{a}{x+1}=1无解，则a=a=___.
  23. 23符号“∣abcd∣\left|\begin{array}{cc}a&b\\ c&d\end{array}\right|”称为二阶行列式，规定它的运算法则为∣abcd∣=ad−bc.\left|\begin{array}{cc}a&b\\ c&d\end{array}\right|=ad-bc.…
  24. 24(1)解方程：1x+2+12x−1=0(2) \dfrac {1}{x+2}+ \dfrac {1}{2x-1}=0(2)解不等式组：{x+9<3(x+1)3x−2⩾1 \begin{cases} \overset{3x-2\geqslant 1}{x+9 < 3(x+1)}\end{cases}…
  25. 25若分式xx+1\dfrac{x}{x+1}的值为00，则xx的值是___.
  26. 262c+b=b−ca2c + b = \frac{b - c}{a} Rearrange the formula to make b the subject. Answer b = ...
  27. 27已知关于xx的分式方程a−1x+2=1 \dfrac {a-1}{x+2}=1无解，则a=a=___．
  28. 28袋中有55个白球，若干个红球，从中任意取一个球，恰为红球的概率是23\dfrac{2}{3}，则红球的个数为()(\quad) A. 44 B. 55 C. 1010 D. 1515
  29. 29已知关于xx的方程2x−mx+2=4 \dfrac {2x-m}{x+2}=4的解是负数，则mm的取值范围为 ___ ．
  30. 30Simplify (a6b38)13×3b−1a2\left(\dfrac{a^6 b^3}{8}\right)^{\tfrac{1}{3}}\times\dfrac{3b^{-1}}{a^2}. Answer ... Solve 2x−2+3x+2=0\dfrac{2}{x-2}+\dfrac{3}{x+2}=0…
  31. 31Solve the inequality 2x−34≤5−x5\frac{2x-3}{4} \le \frac{5-x}{5}. Answer ...
  32. 32如果分式12x−1\dfrac{1}{2x-1}有意义，那么xx的取值范围是()() A. x≠12x\ne \dfrac{1}{2} B. x≠−12x\ne -\dfrac{1}{2} C. x≠0x\neq 0 D. x>12x > \dfrac{1}{2}…
  33. 33代数式8−2xx−2\dfrac{\sqrt{8-2x}}{x-2}有意义，则xx的取值范围是___．
  34. 34A regular polygon has nn sides. When the number of sides is doubled, each of the interior angles is increased by 30°. F…
  35. 35关于xx的分式方程x−3x−2+1=2x−a2−x\dfrac{x-3}{x-2}+1=\dfrac{2x-a}{2-x}的解是正数，则aa的取值范围是 ___.
  36. 36若关于xx的分式方程6x−2−1=ax2−x\dfrac{6}{x-2}-1=\dfrac{ax}{2-x}有增根，则aa的值为()(\quad) A. −3-3 B. 33 C. 22 D. −72-\dfrac{7}{2}…
  37. 37A fraction is such that its denominator is 3 more than its numerator. When 1 is added to both the numerator and denomina…
  38. 38已知函数f(x)=log⁡4x−1x+1(1)f\left(x\right)={{\log}_{4}}\dfrac{x-1}{x+1}(1)若f(a)=12f\left(a\right)=\dfrac{1}{2}，求aa的值； (2)判断f(x)f\left(x\right)…
  39. 39It is given that y=5x−23x+1y=\dfrac{5x-2}{3x+1}. Find yy when x=7x=7. Answer yy = ... Express xx in terms of yy. Answer xx =…
  40. 40若x=3x=3是分式方程a−2x−1x−2=0 \dfrac {a-2}{x}- \dfrac {1}{x-2}=0的根，则aa的值是()() A. 55 B. −5-5 C. 33 D. −3-3
  41. 41Express 12xy215÷2xy3(3x)2\frac{12xy^2}{15} \div \frac{2xy^3}{(3x)^2} as a single fraction in its simplest form. Given that v3=2s+vs−33\dfrac{v}{3} = \sqrt[3]{\dfrac{2s+v}{s-3}}…
  42. 42解下列各题 (1)先化简：(2x−x2+1x)÷x2−2x+1x(2x- \dfrac {x^{2}+1}{x})÷ \dfrac {x^{2}-2x+1}{x}，然后从00，11，−2-2中选择一个适当的数作为xx的值代入求值． (2)解方程：3x+1=xx−1−1 \dfrac {3}{x+1}= \dfrac {x}{x-1}-1…
  43. 43判断代数式(2a2+2aa2−1−a2−aa2−2a+1)÷aa+1(\dfrac{2{{a}^{2}}+2a}{{{a}^{2}}-1}-\dfrac{{{a}^{2}}-a}{{{a}^{2}}-2a+1})\div \dfrac{a}{a+1}的值能否等于−1-1？并说明理由．
  44. 44方程1x−1=2x2−1\dfrac{1}{x-1}=\dfrac{2}{{{x}^{2}}-1}的增根可能是()() A. x=1x=1 B. x=−1x=-1 C. x=1x=1或x=−1x=-1 D. x=2x=2
  45. 45一个不透明的盒子中装有66个黑球和若干个白球，它们除颜色不同外，其余均相同．从盒子中随机摸出一球记下其颜色，再把它放回盒子中摇匀，重复上述过程，共实验300300次，其中有240240次摸到白球．由此估计盒子中的白球大约有 ___…
  46. 46若关于xx的分式方程2x−1=mx\dfrac{2}{x-1}=\dfrac{m}{x}有正整数解，则整数mm的值是 ___.
  47. 47今年我省荔枝喜获丰收，有甲、乙两块面积相同的荔枝园，分别收获8600kg8600kg和9800kg9800kg，甲荔枝园比乙荔枝园平均每亩少60kg60kg，问甲荔枝园平均每亩收获荔枝多少kgkg？设甲荔枝园平均每亩收获荔枝xkgxkg，根据…
  48. 48解下列方程． (1)5x−4x−2=4x+103x−6−1(2)3x+1+2x−1=6x2−1(1)\dfrac{5x-4}{x-2}=\dfrac{4x+10}{3x-6}-1(2)\dfrac{3}{x+1}+\dfrac{2}{x-1}=\dfrac{6}{{{x}^{2}}-1}
  49. 49在一个不透明的盒子中装有55个黑色棋子和若干个白色棋子.每个棋子除颜色外都相同，任意摸出一个棋子，摸到黑色棋子的概率是14\dfrac{1}{4}，则白色棋子的个数是___.
  50. 50通州区运河两岸的“运河绿道”和步行道是健身的主要场地之一.杨师傅分别体验了6060公里的“运河绿道”骑行和1616公里的健步走，已知骑行的平均速度是健步走平均速度的44倍，结果健步走比骑行多用了1212分钟，求杨师傅健步走…
  51. 51某商场购进甲、乙两种服装，每件甲种服装比每件乙种服装贵2525元，该商场用20002000元购进甲种服装，用750750元购进乙种服装，所购进的甲种服装的件数是所购进的乙种服装的件数的22倍． (1)分别求每件甲种服装和每件乙种…
  52. 52已知下列方程：①y−12=y3+1\dfrac{y-1}{2}=\dfrac{y}{3}+1；②x+y=3x+y=3；③x=0x=0；④x2+4x=3x^{2}+4x=3；⑤−3=5x-3=\dfrac{5}{x}；⑥x(1−2x)=3x−1.x(1-2x)=3x-1.其中是…
  53. 53Make x the subject of the given formula 3y=y2x2−1\frac{3}{y} = \sqrt{\frac{y}{2x^2 - 1}}. Answer x = ...
  54. 54当xx___时，分式15−3x\dfrac{1}{5-3x}有意义；当xx___时，分式xx−1\dfrac{x}{x-1}值为00；
  55. 55The gradient of the line joining the points (−3+2a,7)(-3+2a, 7) and (a+1,2)(a+1, 2) is −23-\frac{2}{3}. Find the value of a. Answer a…
  56. 56若分式x−22x+1\dfrac{x-2}{2x+1}的值为零，则xx的值等于()(\quad) A. −3-3 B. 00 C. 22 D. 33
  57. 57若分式x2−9x−3\dfrac{x^{2}-9}{x-3}的值为零，则xx的值为()(\quad) A. −3-3 B. −1-1 C. 33 D. ±3±3
  58. 58解分式方程1x−1−2=31−x \dfrac {1}{x-1}-2= \dfrac {3}{1-x}，去分母得()() A. 1−2(x−1)=−31-2(x-1)=-3 B. 1−2(x−1)=31-2(x-1)=3 C. 1−2x−2=−31-2x-2=-3 D. 1−2x+2=31-2x+2=3…
  59. 59已知关于xx的分式方程2a−1x+1=1 \dfrac {2a-1}{x+1}=1的解是负数，则aa的取值范围是()() A. a<1a < 1 B. a>1a > 1 C. a>1a > 1且a≠2a\neq 2 D. a<1a < 1…