Найдем ОДЗ
\left \{ {{x \neq 3} \atop {x \neq 8}} \right.\\\ \\\
\frac{8}{x-3}+\frac{3}{x-8}=2\\\
\frac{8(x-8)+3(x-3)}{(x-3)(x-8)}=2\\\
8(x-8)+3(x-3)=2(x-8)(x-3)\\\
8x-64+3x-9=2x^2-6x-16x+48\\\
2x^2-22x-11x+48+73=0\\\
2x^2-33x+121=0\\\
D=1089-968=121\\\
x_1=\frac{33+11}{4}=11\ \ \ \ \ \ x_1=\frac{33-11}{4}=5,5" alt=" \left \{ {{x-3 \neq 0} \atop {x-8 \neq 0}} \right. <=> \left \{ {{x \neq 3} \atop {x \neq 8}} \right.\\\ \\\
\frac{8}{x-3}+\frac{3}{x-8}=2\\\
\frac{8(x-8)+3(x-3)}{(x-3)(x-8)}=2\\\
8(x-8)+3(x-3)=2(x-8)(x-3)\\\
8x-64+3x-9=2x^2-6x-16x+48\\\
2x^2-22x-11x+48+73=0\\\
2x^2-33x+121=0\\\
D=1089-968=121\\\
x_1=\frac{33+11}{4}=11\ \ \ \ \ \ x_1=\frac{33-11}{4}=5,5" align="absmiddle" class="latex-formula">