Explicație pas cu pas:
[tex]e(x) = (1 + \frac{1}{x - 2} - \frac{2}{x + 2} ) \div \frac{1}{x {}^{2} - 4} - x {}^{2} + 5x \\ a) \\ x - 2≠0 = > x≠ 2 \\ x + 2≠0 = > x≠ - 2 \\ x {}^{2} - 4≠0 = > x≠2 \\ valori \: nedefinite \: pentru \: x = 2 \: si \: x = - 2 \\ b) \\ \frac{(x - 2)(x + 2) + x + 2 - 2(x - 2)}{(x - 2)(x + 2)} \times \frac{ {x}^{2} - 4}{1} - x {}^{2} + 5x = \\
\frac{x {}^{2} - 4 - x + 6}{x {}^{2} - 4} \times (x {}^{2} - 4) - x {}^{2} + 5x = \\ x {}^{2} - x + 2- {x}^{2} + 5x = \\ 4x + 2 = 2(2x + 1) \\ c) \\ e(x) = 13 \\ 2(2x + 1) = 13 \\ 4x = 11 \\ x = \frac{11}{4} [/tex]
