Question

Решите рациональное уравнение, пожалуйста

Answer 1

$\dfrac{1}{(x-1)^{2} }-\dfrac{5}{x-1} +6=0\\\\\dfrac{1-5(x-1)+6(x^{2}-2x+1) }{(x-1)^{2} } =0\\\\\dfrac{1-5x+5+6x^{2}-12x+6 }{(x-1)^{2} } =0\\\\\dfrac{6x^{2}-17x+12 }{(x-1)^{2} }=0\\\\6x^{2}-17x+12=0 \ , \ x\neq1\\\\D=(-17)^{2}-4*6*12=289-288=1\\\\x_{1} =\frac{17+1}{12}=\frac{18}{12} =1,5\\\\x_{2} =\frac{17-1}{12} =\frac{16}{12} =1\frac{1}{3} \\\\x_{1} \cdot x_{2} =1,5\cdot 1\frac{1}{3}=\frac{3}{2} \cdot \frac{4}{3}=2\\\\\boxed{x_{1} \cdot x_{2} =2}$