Question

Решите уравнение пж, даю 100 баллов ​

Answer 1

$1)frac{4}{9x^{2}-1}-frac{4}{3x+1}-frac{4}{1-3x}=0\\frac{4}{(3x-1)3x+1)}-frac{4}{3x+1}+frac{4}{3x-1}=0\\frac{4-4(3x-1)+4(3x+1)}{(3x-1)(3x+1)}=0\\frac{4-12x+4+12x+4}{(3x-1)(3x+1)}=0\\frac{12}{(3x-1)(3x+1)}=0$

Ответ : x ∈ ∅

$2)frac{4}{y+3}-frac{5}{3-y}=frac{1}{y-3}-1\\frac{4}{y+3}+frac{5}{y-3}-frac{1}{y-3}+1=0\\frac{4(y-3)+5(y+3)-(y+3)+(y-3)(y+3)}{(y-3)(y+3)}=0\\frac{4y-12+5y+15-y-3+y^{2}-9 }{(y-3)(y+3)}=0\\frac{y^{2}+8y-9 }{(y-3)(y+3)}=0\\frac{(y-1)(y+9)}{(y-3)(y+3)}=0\\left { {{(y-1)(y+9)=0} atop {y-3neq0;y+9neq0}} right. \\\y_{1}=1\\y_{2}=-9\\yneq 3;yneq-3\\Otvet:boxed{1;-9}$