Question

Sa se rezolve:$\frac{1}{x-1} + \frac{1}{ (1-x)^{2} } -2=0$

Answer 1

[tex] \frac{-1}{1-x} + \frac{1}{(1-x)^2} - \frac{2(1-x)^2}{(1-x)^2}=0\\ \frac{x-1}{(1-x)^2} + \frac{1}{(1-x)^2} - \frac{2(1-x)^2}{(1-x)^2}=0\\ \frac{x-2+4x-2x^2}{(1-x)^2}=0\\ \frac{-2x^2+5x-2}{(1-x)^2}=0 [/tex]

Conditia de existenta a fractiei - numitorul diferit de 0: 
(1-x)² ≠ 0 ==> x ≠ 1

[tex]-2x^2+5x-2 = 0\\ \Delta=25-16=9 \rightarrow \sqrt{\Delta}=3 \\ x_{1,2}= \frac{-5\pm3}{-4} [/tex]

Solutiile sunt 1/2 si 2