Question

Să se rezolve ecuația (3x-1)/(x+1)+(x+1)/(2x-1)=3
P.S.
Solutia este x apartine(1,5), dar nu stiu cum a dat rezultatul acesta.

Answer 1

$\Rightarrow\;\frac{3x-1}{x+1}+\frac{x+1}{2x-1}=3\\ \frac{(3x-1)(2x-1)+(x+1)(x+1}{(x+1)(2x-1}=3\;\;|\;\cdot(x+1)(2x-1)\\ (3x-1)(2x-1)+(x+1)^2=3(2x-1)(x+1)\\ 6x^2-2x-3x+1+x^2+2x+1=6x^2+6x-3x-3\\ restrangem\;termenii\;asemenea\;\\ \Rightarrow\;\;x^2\,-\;6x+5=0\\ adica:\;x^2-x-5x+5=x(x-1)-5(x-1)=0\\ de\;unde\;\;\\ x-1=0\;\;\rightarrow\;\;x_{1}=1\;si\\ x-5=0\;\;\rightarrow\;\;x_{2}=5\\ deci:\;S(x_{1};x_{2})=(1\,;\,5)$