√[(2x-1)/(x+1)] + 9 √[(x+1)/(2x-1)] =6
пусть t=√[(2x-1)/(x+1)]
тогда √[(x+1)/(2x-1)] =1/t,
t+9/t=6 ⇔ t²-6t+9=0 ⇔ (t-3)²=0 ⇔t=3
или √[(2x-1)/(x+1)]=3 ⇒2x-1 =9(x+1) ⇒ 7x=-10 x=-10/7
проверяем
[2(-10/7)-1]/(-10/7+1)=9
(-10/7+1)/[2(-10/7)-1]=1/9 √(9)+9√(1/9)=3+3=6 верно