Question

Aratati ca    (2SUPRAx-2+xSUPRAx+2) : x²+4SUPRAx²-x-2=x+1SUPRAx+a   pentru orice x ∈ R \ {-2; -1; 2 } 

Answer 1

[2/(x-2)+x/(x+2)]:(x²+4)/(x²-x-2)=(x+1)/x+a
[2(x+2)+x(x-2)]/[(x-2)(x+2)]:(x²+4)/[(x-1)(x+2)=(x+1)/x+a
[2x+4+x²-2x]/[(x-2)(x+2)]·[(x-1)(x-2)/(x²+4)=(x+1)/(x+a)    se simplifica cu x-2
(x²+4)/(x+2)·(x-1)/(x²+4)=(x+1)/(x+a)    se simplifica cu x²+4
(x-1)/(x+2)=(x+1)/(x+a)
(x-1)(x+a)=(x+1)(x+2)
x²+xa-x-a=x²+2x+x+2
x²-x+xa-a=x²+3x+2
x²-x²-x-3x+xa=2+a
-4x+xa=2+a
x(a-4)=a+2
x=(a+2)/(a-4)