Step-by-step explanation:
[tex] \frac{2}{x - y} + \frac{3}{x + y} - \frac{5}{y - x} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ \\ = \frac{2}{x - y} + \frac{3}{x + y} + \frac{5}{x - y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ \\ = \frac{7}{x - y} + \frac{3}{x + y} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ \\ = \frac{7x + 7y + 3x - 3y}{(x - y)(x + y)} - \frac{7x - 9y}{ {y}^{2} - {x}^{2} } \\ \\ = \frac{10x + 4y}{ {x}^{2} - {y}^{2} } + \frac{7x - 9y}{ {x}^{2} - {y}^{2} } \\ \\ = \frac{17x - 5y}{ {x}^{2} - {y}^{2} } \\ \\ = \frac{ \red{ \boxed{ \bold{5y - 17x}}}}{ {y}^{2} - {x}^{2} } [/tex]
