Question

Se considera expresia...
Vă rog ajutați-mă!!
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Answer 1

Explicație pas cu pas:

a)

$E(x) = \left(\frac{ {x}^{3} - 2 {x}^{2}}{2 {x}^{2} } - \frac{ {x}^{2} - 4}{4x} \right) \div \frac{x - 2}{2} + \frac{1}{2} \\ = \left(\frac{ 2{x}^{2}(x - 2)}{4{x}^{2} } - \frac{(x - 2)(x + 2)}{4x} \right) \times \frac{2}{x - 2} + \frac{1}{2} \\ = \frac{ 2x(x - 2) - (x - 2)(x + 2)}{4x} \times \frac{2}{x - 2} + \frac{1}{2} \\ = \frac{(x - 2)(2x - x - 2)}{2x} \times \frac{1}{x - 2} + \frac{1}{2} \\ = \frac{x - 2}{2x} + \frac{1}{2} = \frac{1}{2} - \frac{1}{x} + \frac{1}{2} = 1 - \frac{1}{x}$

b)

$E(3) \times E(4) \times E(5) \times E(6) \times E(7) \times E(8) = \\ = \left(1 - \frac{1}{3} \right)\left(1 - \frac{1}{4} \right)\left(1 - \frac{1}{5} \right)\left(1 - \frac{1}{6}\right)\left(1 - \frac{1}{7} \right)\left(1 - \frac{1}{8}\right) \\ = \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times \frac{7}{8} = \frac{2}{8} = \frac{1}{4}$