Ответ:
[tex]\dfrac{x-3}{x+2}+\dfrac{x+2}{x-3}=4\dfrac{1}{4}\ \ ,\ \ \ ODZ:\ x\ne -2\ ,\ x\ne -3\ ,[/tex]
Умножим уравнение на 4(x+2)(x-3)≠0 .
[tex]4(x-3)^2+4(x+2)^2=17(x+2)(x-3)\\\\4(x^2-6x+9)+4(x^2+4x+4)=17(x^2-3x+2x-6)\\\\4x^2-24x+36+4x^2+16x+16-17x^2+17x+102=0\\\\-9x^2+9x+154=0\ \ ,\\\\9x^2-9x-154=0\\\\D=b^2-4ac=9^2+4\cdot 9\cdot 154=81+5544=5625=75^2\\\\x_1=\dfrac{9-75}{18}=-\dfrac{66}{18}=-\dfrac{11}{3}=-3\dfrac{2}{3}\\\\x_2=\dfrac{9+75}{18}=\dfrac{84}{18}=\dfrac{14}{3}=4\dfrac{2}{3}[/tex]
Ответ: [tex]x=-3\dfrac{2}{3}\ \ ,\ \ x_2=4\dfrac{2}{3}\ .[/tex]
