Question

Aflati valorile întregi ale lui x,x apartine R\{4;0} Pentru care valoarea expresiei E(x)=x^2+x-12/x^2+4x - x+1/x.Este un nr natural
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Answer 1

 

$\displaystyle\\E(x)=\frac{x^2+x-12}{x^2+4x}-\frac{x+1}{x}\\\\E(x)=\frac{x^2+4x-3x-12}{x^2+4x}-\frac{x+1}{x}\\\\E(x)=\frac{x(x+4)-3(x+4)}{x(x+4)}-\frac{x+1}{x}\\\\E(x)=\frac{(x+4)(x-3)}{x(x+4)}-\frac{x+1}{x}\\\\E(x)=\frac{x-3}{x}-\frac{x+1}{x}\\\\E(x)=\frac{x-3-(x+1)}{x}\\\\E(x)=\frac{x-3-x-1}{x}\\\\E(x)=\frac{-3-1}{x}\\\\E(x)=\frac{-4}{x}\\\\ x~\text{ este divizor intreg al lui -4 a.i. }~E(x)\in~N\\\\\implies~x~\text{divizor negativ al lui -4.}\\\\\bf~x\in\{-1;~-2\}\\x=-4~nu~este~admisa$