Quy đồng mẫu thức nhiều phân thức

Câu hỏi trắc nghiệm

Chủ đề: Quy đồng mẫu thức nhiều phân thức

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:

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


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