Quy đồng mẫu thức các phân thức sau:
a) \(\frac{4x^2-3x+5}{x^3-1};\frac{2x}{x^2+x+1};\frac{x}{x-1}\)
\(=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)};\frac{2x\left(x-1\right)}{\left(x^2+x+1\right).\left(x-1\right)};\frac{x\left(x^2+x+1\right)}{\left(x-1\right).\left(x^2+x+1\right)}\)
\(=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)};\frac{2x^2-2x}{\left(x-1\right)\left(x^2+x+1\right)};\frac{x^3+x^2+x}{\left(x-1\right)\left(x^2+x+1\right)}\)
b, \(\frac{4}{x+2};\frac{3}{x-2};\frac{5x+2}{4-x^2}\)
\(=\frac{4}{x+2};\frac{3}{x-2};\frac{5x+2}{\left(2-x\right)\left(2+x\right)}\)
\(=\frac{4\left(x-2\right)}{\left(x+2\right).\left(x-2\right)};\frac{3\left(x+2\right)}{\left(x-2\right).\left(x+2\right)};\frac{-5x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x-8}{\left(x+2\right)\left(x-2\right)};\frac{3x+6}{\left(x-2\right)\left(x+2\right)};\frac{-5x-2}{\left(x-2\right)\left(x+2\right)}\)
