[tex] \dfrac{2}{x - 2} + \dfrac{7}{ {x}^{2} - 4 } = \dfrac{5}{x} \\ \\ \dfrac{2}{x - 2} + \dfrac{7}{(x - 2)(x + 2)} = \dfrac{5}{x} \\ \\ \dfrac{2x(x + 2) + 7x}{x(x - 2)(x + 2)} = \dfrac{5(x - 2)(x + 2)}{x(x - 2)(x + 2)} \\ \\ {2x}^{2} + 4x + 7x = {5x}^{2} - 20 \\ {3x}^{2} - 11x = 20 \\ {3x}^{2} - 11x - 20 = 0 \\ (3x + 4)(x - 5) = 0[/tex]
3x + 4 = 0 or x - 5 = 0
Answer :
[tex]x = - 1 \dfrac{1}{3} \: or \: x = 5[/tex]
Hope this helps. - M
