Question

Se da expresia E(x)=(2\x-3-3\xpatrat-9+4\x+3)*(2x-3\4x-12)patrat
a) aduceti expresia la forma cea mai simpla
b)pt ce numere reale x, E(x) nu are sens?
c)Determinati numerele naturale x, pentru care E(x) este natural.

Answer 1

$E(x)= (\frac{2}{x-3} - \frac{3}{(x-3)(x+3)} + \frac{4}{x+3} )( \frac{2x-3}{4(x-3)})^{2} } \\ \frac{2x+6-3+4x-12}{(x+3)(x-3)} ( \frac{2x-3}{4(x-3)} )^{2} = \frac{3(x-3)}{(x+3)(x-3)}. \frac{ (2x-3)^{2} }{16 (x-3)^{2} }= \frac{3 (2x-3)^{2} }{16(x+3). (x-3)^{2} }$
$b)x \neq 3,-3$