Question

С2. Решите уравнение: 8/(y ^ 2 - 4) + 7/(y + 2) = y/(y - 2)​

Answer 1

Объяснение:

ОДЗ: y+2≠0      y≠-2       y-2≠0      y≠2.

$\displaystyle\\\frac{8}{y^2-4}+\frac{7}{y+2} =\frac{y}{y-2} \\\\\frac{8}{(y+2)*(y-2)}+\frac{7}{y+2} =\frac{y}{y-2} \\\\8+7*(y-2)=y*(y+2)\\\\8+7y-14=y^2+2y\\\\y^2-5y+6=0\\\\y^2-2y-3y+6=0\\\\y*(y-2)-3*(y-2)=0\\\\(y-2)*(y-3)=0\\\\y-2=0\\\\y_1=2\notin.\\\\y-3=0\\\\y_2=3.$

Ответ: y=3.