[tex]10. \: \frac{2 {x}^{2} - x }{3x + 3} + \frac{2x - 1}{3x - 3} \\ = \frac{(2 {x}^{2} - x)(3x - 3) + (2x - 1)(3x + 3) }{(3x - 3)(3x + 3)} \\ = \frac{6 {x}^{3} - 9 {x}^{2} + 3x + 6 {x}^{2} + 3x - 3 }{9 {x}^{2} - 9 } \\ = \frac{6 {x}^{3} - 3 {x}^{2} + 6x - 3 }{9 {x}^{2} - 9} \\ = \frac{2 {x}^{3} - {x}^{2} + 2x - 1}{3 {x}^{2} - 3 } \\ \\ 11. \: \frac{x + 4}{ {x}^{2} - 1} + \frac{x + 4}{x + 1} \\ = \frac{x + 4 }{(x - 1)(x + 1)} + \frac{(x - 1)(x + 4)}{(x - 1)(x + 1)} \\ = \frac{x + 4 + {x}^{2} + 3x - 4}{ {x}^{2} - 1 } \\ = \frac{ {x}^{2} + 4x}{ {x}^{2} - 1} [/tex]
