\(\dfrac{x+1}{x-6}+3x=\dfrac{x-5}{x^2+6}\left(\text{ĐKXĐ: x\ne}6\right)\\ \dfrac{\left(x+1\right)\left(x^2+6\right)+3x\left(x-6\right)\left(x^2+6\right)}{\left(x-6\right)\left(x^2+6\right)}=\dfrac{\left(x-5\right)\left(x-6\right)}{\left(x-6\right)\left(x^2+6\right)}\\ \Leftrightarrow\left(x+1\right)\left(x^2+6\right)+3x\left(x-6\right)\left(x^2+6\right)=\left(x-5\right)\left(x-6\right)\\ x^3+x^2+6x+6+3x^4-18x^3+18x^2-108x=3x^4-17x^3+19x^2-102x+6=x^2-11x+30\\ 3x^4-17x^3+19x^2-102x+6=x^2-11x+30\\ 3x^4-17x^3+18x^2-91x-24=0\\ \)
bấm máy tính giải phương trình bậc 4 ta được
x1 = 5,606836549
x2 = -0,2485256302
x3 = 0,1541778737 + 2,391109243i
x4 = 0,1541778737 - 2,391109243i
