Răspuns:
E(x) = - 2x
Explicație pas cu pas:
[tex]E(x) = \left( \frac{2}{x + 3} - \frac{5}{x - 3} + \frac{12}{ {x}^{2} - 9} \right) \div \left( \frac{3}{2x(x - 3)} \right) \\ [/tex]
[tex]= \left( \frac{2(x - 3)}{(x + 3)(x - 3)} - \frac{5(x + 3)}{(x - 3)(x + 3)} + \frac{12}{(x - 3)(x + 3)} \right) \div \left( \frac{3}{2x(x - 3)} \right) \\ [/tex]
[tex]= \left( \frac{2x - 6 - 5x - 15 + 12}{(x + 3)(x - 3)}\right) \times \left( \frac{2x(x - 3)}{3} \right) \\ [/tex]
[tex]= \left( \frac{ - 3x - 9 }{(x + 3)(x - 3)}\right) \times \left( \frac{2x(x - 3)}{3} \right) \\ [/tex]
[tex]= \left( \frac{ - 3(x + 3) }{(x + 3)(x - 3)}\right) \times \frac{2x(x - 3)}{3}\\ [/tex]
[tex]= - 2x [/tex]
