Tổng hợp bài tập trắc nghiệm rèn luyện tư duy chuyên đề Phân thức đại số

  1. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
    Quy đồng mẫu thức \(\dfrac{x^2+2x+5}{x^3+1},\dfrac{3x-1}{x^2-x+1},-3\)
    • \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{3x^2+2x-1}{x^3+1}\); \(\dfrac{-3\left(x^3+1\right)}{x^3+1}\)
    • \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{3x^2+2x+2}{x^3+1}\); \(\dfrac{3\left(x^3+1\right)}{x^3+1}\)
    • \(\dfrac{x^2+2x+5}{x^3+1};\dfrac{2x^2+2x+2}{x^3+1};-\dfrac{3\left(x^2+1\right)}{x^2+1}\)
    • \(\dfrac{x^2+2x}{x^2-x+1};\dfrac{3x-1}{x^2-x+1};\dfrac{-3\left(x^2-x+1\right)}{x^2-x+1}\)
    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.
    \(\dfrac{3x-1}{x^2-x+1}=\dfrac{\left(x+1\right)\left(3x-1\right)}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{3x^2+2x-1}{x^3+1}\)
    \(-3=\dfrac{-3\left(x^3+1\right)}{x^3+1}\)
     
  2. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
    Quy đồng mẫu thức hai phân thức \(\dfrac{5}{3x^3-12x}\) và \(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}\)
    • \(\dfrac{10\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\) và \(\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)
    • \(\dfrac{10}{6x\left(x+2\right)\left(x-2\right)}\) và \(\dfrac{9\left(x-2\right)}{6x\left(x+2\right)\left(x-2\right)}\)
    • \(\dfrac{10x}{6x\left(x+2\right)\left(x-2\right)\left(x+3\right)}\) và \(\dfrac{9\left(x-2\right)\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)
    • \(\dfrac{5\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\) 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 = \(6x\left(x+3\right)\left(x+2\right)\left(x-2\right)\).
    \(\dfrac{5}{3x\left(x-2\right)\left(x+2\right)}=\dfrac{5.2.\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}=\dfrac{10\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\).
    \(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}=\dfrac{3}{2\left(x+2\right)\left(x+3\right)}=\dfrac{3.3x.\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)\(=\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)
     
  3. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
    Quy đồng mẫu thức ba phân thức \(\dfrac{1}{x^2+4x+3};\dfrac{1}{x^2+5x+4};\dfrac{1}{x^2+7x+12}\)
    • \(\dfrac{x+4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{x+3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).
    • \(\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\)
    • \(\dfrac{x+4}{\left(x+1\right)\left(x+3\right)};\dfrac{x+3}{\left(x+1\right)\left(x+4\right)};\dfrac{x+1}{\left(x+3\right)\left(x+4\right)}\)
    • \(\dfrac{4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)};\dfrac{1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\)
    Hướng dẫn giải:

    \(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}\); \(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}\); \(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}\).
    \(MSC=\left(x+1\right)\left(x+3\right)\left(x+4\right)\).
    \(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}=\dfrac{x+4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\);
    \(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}=\dfrac{x+3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\);
    \(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}=\dfrac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).
     
  4. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
    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 mẫu số chung được chọn có thể là biểu thức nào trong số các biểu thức dưới đây?
    • \(3\left(x-1\right)^3\)
    • \(\left(x-1\right)^3\)
    • \(3\left(x+1\right)^3\)
    • \(x^3-1\)
    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 = \(3\left(x-1\right)^3\)
     
  5. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
  6. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
  7. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
  8. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
  9. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
  10. Tác giả: LTTK CTV
    Đánh giá: ✪ ✪ ✪ ✪ ✪
    Thực hiện phép tính \(\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{x}{2x+4}\)
    • \(\dfrac{2x^2+x+4}{4x\left(x+2\right)}\)
    • \(\dfrac{1}{2x}\)
    • \(\dfrac{3x+4}{4x\left(x+2\right)}\)
    • \(\dfrac{2x+5}{4x\left(x+2\right)}\)
    Hướng dẫn giải:

    \(\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{x}{2x+4}\)
    \(=\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{x}{2\left(x+2\right)}\)
    \(=\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{2x^2}{4x\left(x+2\right)}\)
    \(=\dfrac{2x^2+x+4}{4x\left(x+2\right)}\)