Question

va rog ajutati-ma este urgent​

Answer 1

Explicație pas cu pas:

2.

$E_{1} = \frac{ {2}^{2x} + {2}^{x} - 2}{{2}^{2x} - 3 \cdot {2}^{x} + 2} = \frac{({2}^{x} + 2)({2}^{x} - 1)}{({2}^{x} - 2)({2}^{x} - 1)} = \\ = \frac{{2}^{x} + 2}{{2}^{x} - 2}$

$E_{2} = \frac{ {2}^{3x} - 3 \cdot {2}^{x} + 2}{{2}^{2x} - 1}$

notăm:

${2}^{x} = t > 0$

$E_{2} = \frac{ {t}^{3} - 3 \cdot t + 2}{{t}^{2} - 1} = \frac{ {t}^{3} + 2 \cdot {t}^{2} - 2 \cdot {t}^{2} - 4 \cdot t + t + 2}{(t - 1)(t + 1)} = \\ = \frac{ {t}^{2}(t + 2) - 2t(t + 2) + t + 2}{(t - 1)(t + 1)} = \frac{ (t + 2)({t}^{2} - 2t + 1)}{(t - 1)(t + 1)} \\ = \frac{ (t + 2) {(t - 1)}^{2} }{(t - 1)(t + 1)} = \frac{ (t + 2) (t - 1)}{t + 1}$

=>

$E_{2} = \frac{ ({2}^{x} + 2) ({2}^{x} - 1)}{{2}^{x} + 1}$