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[tex]E(x)= \frac{x^4+x^2+1}{(x+1)^2-x}[/tex]
Va rog sa-mi explicati


Răspuns :

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