Question

Fie expresia Ex=x-(1supra x-3 + 7-x2 totul supra x-1 x(ori) 1/x-3) : x+2 totul supra 2(x-1) , unde x apartine R/{-2,1,3}
a) Aratati ca Ex=x+2
b) Determinati valorile lui x pentru care Ex +2radical6=1 supra Ex - 2radical6
c) Determinati valorile lui a pentru care 1-E(a radical2)

Answer 1

$a)Ex=x-( \frac{1}{x-3}+ \frac{7- x^{2} }{x-1}* \frac{1}{x-3}): \frac{x+2}{2(x-1)}= \\ =x-( \frac{1}{x-3}+ \frac{7- x^{2} }{(x-1)(x-3)}): \frac{x+2}{2(x-1)}= \\ =x-( \frac{x-1+7- x^{2} }{(x-1)(x-3)}): \frac{x+2}{2(x-1)}= \\ =x- \frac{-( x^{2}-x-6) }{(x-1)(x-3)}* \frac{2(x-1)}{x+2}=x+ \frac{(x-3)(x+2)}{(x-1)(x-3)}* \frac{2(x-1)}{x+2}= \\ =x+2$