Quy đồng mẫu thức nhiều phân thức

Câu hỏi trắc nghiệm

Chủ đề: Quy đồng mẫu thức nhiều phân thức

Câu 1.

Để quy đồng hai phân thức \(\dfrac{A}{2x^3y^2}\) và \(\dfrac{2B}{3xy^4z}\) ta chọn mẫu số chung là biểu thức nào dưới đây?​

  1. \(6x^3y^4z\).
  2. \(12x^3y^5\).
  3. \(24x^2y^5z\).
  4. \(6xyz\).

Câu 2.

Khi quy đồng mẫu thức hai phân thức \(\dfrac{5}{x^3y^2z}\)  và \(\dfrac{11}{6x^2y^2z^2}\) , ta có kết quả là

  1. \(\dfrac{30z}{6x^3y^2z^2}\) và \(\frac{11x}{6x^3y^2z^2}\).
  2. \(\dfrac{5z}{6x^3y^2z^2}\) và \(\dfrac{11z}{6x^3y^2z^2}\).
  3. \(\dfrac{6z}{6x^3y^2z^2}\) và \(\dfrac{z}{6x^3y^2z^2}\).
  4. \(\dfrac{15z}{6x^3y^2z^2}\) và \(\dfrac{66z}{6x^3y^2z^2}\).

Hướng dẫn giải:

​MSC = \(6x^3y^2z^2\)
\(\dfrac{5}{x^3y^2z}=\dfrac{5.6.z}{6x^3y^2z^2}=\dfrac{30z}{6x^3y^2z^2}\)
\(\dfrac{11}{6x^2y^2z^2}=\dfrac{11x}{6x^3y^2z^2}\)

Câu 3.

Khi quy đồng mẫu thức hai phân thức \(\dfrac{7}{3x+9}\) và \(\dfrac{2x}{x^2+6x+9}\), ta có kết quả là

  1. \(\dfrac{7\left(x+3\right)}{3\left(x+3\right)^2}\) và \(\dfrac{6x}{3\left(x+3\right)^2}\).
  2. \(\dfrac{7\left(x+3\right)}{\left(x+3\right)^2}\) và \(\dfrac{2x}{\left(x+3\right)^2}\).
  3. \(\dfrac{7\left(x-3\right)}{\left(x+3\right)^2}\) và \(\dfrac{6x}{3\left(x+3\right)^2}\).
  4. \(\dfrac{21\left(x+3\right)}{3\left(x+3\right)^2}\) và \(\dfrac{18x}{3\left(x+3\right)^2}\).

Hướng dẫn giải:

​\(\dfrac{7}{3x+9}=\dfrac{7}{3\left(x+3\right)}\); \(\dfrac{2x}{x^2+6x+9}=\dfrac{2x}{\left(x+3\right)^2}\)
MSC: \(3\left(x+3\right)^2\)
\(\dfrac{7}{3\left(x+3\right)}=\dfrac{7\left(x+3\right)}{3\left(x+3\right)^2}\); \(\dfrac{2x}{x^2+6x+9}=\dfrac{2x}{\left(x+3\right)^2}=\dfrac{3.2x}{3\left(x+3\right)^2}=\dfrac{6x}{3\left(x+3\right)^2}\)

Câu 4.

Khi quy đồng mẫu thức của \(\frac{x^2+2x+5}{x^3+1};\frac{3x-1}{x^2-x+1};-3\) , ta có kết quả là

  1. \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{3x^2+2x-1}{x^3+1}\); \(\dfrac{-3\left(x^3+1\right)}{x^3+1}\).
  2. \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{3x^2+2x+2}{x^3+1}\); \(\dfrac{3\left(x^3+1\right)}{x^3+1}\).
  3. \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{2x^2+2x+2}{x^3+1};-\dfrac{3\left(x^2+1\right)}{x^2+1}\).
  4. \(\dfrac{x^2+2x}{x^2-x+1};\dfrac{3x-1}{x^2-x+1};\dfrac{-3\left(x^2-x+1\right)}{x^2-x+1}\).

Hướng dẫn giải:

MSC \(=x^3+1=\left(x+1\right)\left(x^2-x+1\right)\)
​\(\dfrac{x^2+2x+5}{x^3+1}\) giữ nguyên.
\(\dfrac{3x-1}{x^2-x+1}=\dfrac{\left(x+1\right)\left(3x-1\right)}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{3x^2+2x-1}{x^3+1}\)
\(-3=\dfrac{-3\left(x^3+1\right)}{x^3+1}\)

Câu 5.

Khi quy đồng mẫu thức hai phân thức \(\dfrac{5}{3x^3-12x}\) và \(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}\) , ta có kết quả là​

  1. \(\dfrac{10\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\) và \(\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\).
  2. \(\dfrac{10}{6x\left(x+2\right)\left(x-2\right)}\) và \(\dfrac{9\left(x-2\right)}{6x\left(x+2\right)\left(x-2\right)}\).
  3. \(\dfrac{10x}{6x\left(x+2\right)\left(x-2\right)\left(x+3\right)}\) và \(\dfrac{9\left(x-2\right)\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\).
  4. \(\dfrac{5\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\) và \(\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\).

Hướng dẫn giải:

​\(\dfrac{5}{3x^3-12x}=\dfrac{5}{3x\left(x^2-4\right)}=\dfrac{5}{3x\left(x-2\right)\left(x+2\right)}\)
\(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}=\dfrac{3}{2\left(x+2\right)\left(x+3\right)}\)
MSC = \(6x\left(x+3\right)\left(x+2\right)\left(x-2\right)\).
\(\dfrac{5}{3x\left(x-2\right)\left(x+2\right)}=\dfrac{5.2.\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}=\dfrac{10\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\).
\(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}=\dfrac{3}{2\left(x+2\right)\left(x+3\right)}=\dfrac{3.3x.\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)\(=\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)

Câu 6.

Khi quy đồng mẫu thức ba phân thức \(\dfrac{1}{x^2+4x+3};\dfrac{1}{x^2+5x+4};\dfrac{1}{x^2+7x+12}\), ta có kết quả là​

  1. \(\dfrac{x+4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{x+3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).
  2. \(\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).
  3. \(\dfrac{x+4}{\left(x+1\right)\left(x+3\right)};\dfrac{x+3}{\left(x+1\right)\left(x+4\right)};\dfrac{x+1}{\left(x+3\right)\left(x+4\right)}\).
  4. \(\dfrac{4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).

Hướng dẫn giải:

​\(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}\); \(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}\); \(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}\).
\(MSC=\left(x+1\right)\left(x+3\right)\left(x+4\right)\).
\(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}=\dfrac{x+4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\);
\(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}=\dfrac{x+3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\);
\(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}=\dfrac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).

Câu 7.

Khi quy đồng mẫu thức các phân thức \(\dfrac{2x+3}{x^3-3x^2+3x-1};\dfrac{x^2}{x^2-2x+1};\dfrac{1}{3x-3}\) thì biểu thức nào sau đây được chọn làm mẫu số chung?

  1. \(3\left(x-1\right)^3\).
  2. \(\left(x-1\right)^3\).
  3. \(3\left(x+1\right)^3\).
  4. \(x^3-1\).

Hướng dẫn giải:

​\(x^3-3x^2+3x-1=\left(x-1\right)^3\);
\(x^2-2x+1=\left(x-1\right)^2\)
\(3x-3=3\left(x-1\right)\).
MSC = \(3\left(x-1\right)^3\)


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