Question

решите уравнение х-3/х - х+5/х-3 = 3

Answer 1

ОДЗ : x ≠ 0         x - 3 ≠ 0  ⇒ x ≠ 3

$\frac{x-3}{x}- \frac{x+5}{x-3} =3\\\\ \frac{ x^{2} -6x+9- x^{2} -5x}{x(x-3)} =3\\\\ \frac{9-11x}{ x^{2} -3x} -3=0\\\\ \frac{9-11x-3 x^{2} +9x}{x(x-3)} =0\\\\ \frac{3 x^{2} +2x-9}{x(x-3)}=0\\\\3 x^{2} +2x-9=0\\\\D=2 ^{2}-4*3*(-9)=4+108=112\\\\ x_{1}= \frac{-2+ \sqrt{112} }{6}= \frac{-2+4 \sqrt{7} }{6}= \frac{-1+2 \sqrt{7} }{3}\\\\ x_{2}= \frac{-2- \sqrt{112} }{6}= \frac{-2-4 \sqrt{7} }{6} = \frac{-1-2 \sqrt{7} }{3}$