Question

Exercițiul 5 (este însemnat) doar punctul a

Answer 1

$E(x) = ( \frac{2}{x} + \frac{1}{ {x}^{2} }) \times {( \frac{ {3x}^{2} + 5x + 2 }{ {x}^{3} + {x}^{2} }) }^{ - 1} \\ \\ E(x) = \frac{2x + 1}{ {x}^{2} } \times {( \frac{ {3x}^{2} + 3x + 2x + 2 }{ {x}^{2}(x + 1) }) }^{ - 1} \\ \\ E(x) = \frac{2x + 1}{ {x}^{2} } \times {( \frac{3x(x + 1) + 2(x + 1)}{ {x}^{2}(x + 1) }) }^{ - 1} \\ \\ E(x) = \frac{2x + 1}{ {x}^{2} } \times {( \frac{(x + 1)(3x + 2)}{ {x}^{2}(x + 1) }) }^{ - 1} \\ \\ E(x) = \frac{2x + 1}{ {x}^{2} } \times {( \frac{3x + 2}{ {x}^{2} }) }^{ - 1} \\ \\ E(x) = \frac{2x + 1}{ {x}^{2} } \times \frac{ {x}^{2} }{3x + 2} \\ \\ E(x) = (2x + 1) \times \frac{1}{3x + 2} \\ \\ E(x) = \frac{(2x + 1) \times 1}{3x + 2} \\ \\ E(x) = \frac{2x + 1}{3x + 2}$