[tex] \frac{6x}{x + 1} + \frac{16}{ {x}^{2} + x } = \frac{11}{x} \\ \frac{6x}{x + 1} + \frac{16}{x(x + 1)} = \frac{11}{x} \\ 6 {x}^{2} + 16 = 11(x + 1) \\ 6 {x }^{2} + 16 = 11x + 11 \\ 6 {x}^{2} - 11x + 5 = 0 \\ d = ( - 11) {}^{2} - 4 \times 6 \times 5 = 121 - 120 = 1 \\ x = \frac{11 + 1}{12} = \frac{12}{12} = 1 \\ x = \frac{11 - 1}{12} = \frac{10}{12} = \frac{5}{6} [/tex]