Question

Дробь 3/(x-2)^2+дробь 5/(x-2)-8=0

Answer 1

$frac{3}{(x-2)^2}+frac{5}{x-2}-8=0\\frac{3}{(x-2)^2}+frac{5(x-2)}{(x-2)^2}-frac{8(x-2)^2}{(x-2)^2}=0\\frac{3+5(x-2)-8(x-2)^2}{(x-2)^2}=0\\frac{3+5x-10-8(x^2-4x+4)}{(x-2)^2}=0\\frac{3+5x-10-8x^2+32x-32}{(x-2)^2}=0\\frac{-8x^2+37x-39}{(x-2)^2}=0\\ left { {{-8x^2+37x-39=0} atop {(x-2)^2 neq 0}} right. left { {{-8x^2+37x-39=0} atop {x-2 neq 0}} right. left { {{-8x^2+37x-39=0} atop {x neq 2}} right.$
О Отдельно решим первое уравнение системы
$-8x^2+37x-39=0|:(-1)\8x^2-37x+39=0\D=(-37)^2-4*8*39=1369-1248=121\x_{1}=frac{37+11}{16}=frac{48}{16}=3\\x_{2}=frac{37-11}{16}=frac{26}{16}=frac{13}{8}=1frac{5}{8}$
Вернемся в систему
$1.left { {{x=3} atop {x neq 2}} right= textgreater x=3\\2,left { {{x=1frac{5}{8}} atop {x neq 2}} right.= textgreater x=1frac{5}{8}$
$Otvet:x=3,x=1frac{5}{8}$