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