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. \(\dfrac{3x-1}{x^2-x+1}=\dfrac{\left(x+1\right)\left(3x-1\right)}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{3x^2+2x-1}{x^3+1}\) \(-3=\dfrac{-3\left(x^3+1\right)}{x^3+1}\)
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 = \(6x\left(x+3\right)\left(x+2\right)\left(x-2\right)\). \(\dfrac{5}{3x\left(x-2\right)\left(x+2\right)}=\dfrac{5.2.\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}=\dfrac{10\left(x+3\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\). \(\dfrac{3}{\left(2x+4\right)\left(x+3\right)}=\dfrac{3}{2\left(x+2\right)\left(x+3\right)}=\dfrac{3.3x.\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)\(=\dfrac{9x\left(x-2\right)}{6x\left(x+3\right)\left(x+2\right)\left(x-2\right)}\)
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: \(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}\); \(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}\); \(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}\). \(MSC=\left(x+1\right)\left(x+3\right)\left(x+4\right)\). \(\dfrac{1}{x^2+4x+3}=\dfrac{1}{\left(x+1\right)\left(x+3\right)}=\dfrac{x+4}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\); \(\dfrac{1}{x^2+5x+4}=\dfrac{1}{\left(x+1\right)\left(x+4\right)}=\dfrac{x+3}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\); \(\dfrac{1}{x^2+7x+12}=\dfrac{1}{\left(x+3\right)\left(x+4\right)}=\dfrac{x+1}{\left(x+1\right)\left(x+3\right)\left(x+4\right)}\).
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 = \(3\left(x-1\right)^3\)
Thực hiện phép tính \(\dfrac{2x+1}{4x+5}+\dfrac{3}{4x+5}\) \(\dfrac{2x+4}{4x+5}\) \(\dfrac{6x+3}{4x+5}\) \(\dfrac{2x-4}{4x+5}\) \(\dfrac{2x+3}{4x+5}\)
Thực hiện phép tính : \(\dfrac{x}{x^2-y^2}+\dfrac{-y}{x^2-y^2}\) \(\dfrac{1}{x+y}\) \(\dfrac{1}{x-y}\) \(\dfrac{xy}{x^2-y^2}\) \(-\dfrac{xy}{x^2-y^2}\) Hướng dẫn giải: \(\dfrac{x}{x^2-y^2}+\dfrac{-y}{x^2-y^2}=\dfrac{x-y}{x^2-y^2}=\dfrac{x-y}{\left(x-y\right)\left(x+y\right)}=\dfrac{1}{x+y}\)
Thực hiện phép tính \(\dfrac{x-1}{x+10}+\dfrac{x+8}{x+10}+\dfrac{x+3}{x+10}\) \(\dfrac{3x+10}{x+10}\) \(\dfrac{x+9}{x+10}\) \(\dfrac{x+11}{x+10}\) \(\dfrac{x+12}{x+10}\) Hướng dẫn giải: \(\dfrac{x-1}{x+10}+\dfrac{x+8}{x+10}+\dfrac{x+3}{x+10}=\dfrac{x-1+x+8+x+3}{x+10}=\dfrac{3x+10}{x+10}\)
Thực hiện phép tính \(\dfrac{4xy-3y}{3x^2y^4}+\dfrac{5xy+3y}{3x^2y^4}\) \(\dfrac{3}{xy^3}\) \(\dfrac{3+x}{xy^3}\) \(\dfrac{3x}{xy^3}\) \(\dfrac{3-x}{xy^3}\) Hướng dẫn giải: \(\dfrac{4xy-3y}{3x^2y^4}+\dfrac{5xy+3y}{3x^2y^4}=\dfrac{4xy-3y+5xy+3y}{3x^2y^4}=\dfrac{9xy}{3x^2y^4}=\dfrac{3}{xy^3}\)
Thực hiện phép tính \(\dfrac{2x-3}{x-1}+\dfrac{4x-6}{1-x}+\dfrac{2+x^2}{x-1}\) \(\dfrac{x^2-2x+5}{x-1}\) \(x-1\) \(\dfrac{x^2-2x-1}{x-1}\) \(x+1\) Hướng dẫn giải: \(\dfrac{2x-3}{x-1}+\dfrac{4x-6}{1-x}+\dfrac{2+x^2}{x-1}\)\(=\dfrac{2x-3}{x-1}+\dfrac{6-4x}{x-1}+\dfrac{2+x^2}{x-1}\) \(=\dfrac{2x-3+6-4x+2+x^2}{x-1}\) \(=\dfrac{x^2-2x+5}{x-1}\).
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: \(\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{x}{2x+4}\) \(=\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{x}{2\left(x+2\right)}\) \(=\dfrac{x+4}{4x\left(x+2\right)}+\dfrac{2x^2}{4x\left(x+2\right)}\) \(=\dfrac{2x^2+x+4}{4x\left(x+2\right)}\)