Question

E(x)=$\frac{(2x+1) ^{2}-(2x-1) ^{2} }{(x-1) ^{2}-(x+1)^2 }$ .
unde x este numar real . x diferit de 0 . Aratati ca E(x)=-2

Answer 1

4x^2+4x+1-4x^2+4x-1/ x^2-2x+1-x^2-2x-1=8x/-4x, deci E(x)=-2, ceea ce trebuia de demonstrat!

Answer 2

[tex]\mathrm{E(x)=\frac{(2x+1)^2-(2x-1)^2}{(x-1)^2-(x+1)^2}}} \\ \\ \mathrm{E(x)=\frac{\not 4x^2+4x\not +1-\not 4x^2\not -1+4x}{\not x^2-2x+\not 1-\not x^2-\not1-2x}} \\ \\ \mathrm{E(x)\frac{4x+4x}{-2x-2x}} \\ \\ \mathrm{E(x)=-\frac{8x}{4x}} \\ \\ \boxed{\mathrm{E(x)=-2}}[/tex]