Verified answer

[tex]1. \: \: \: \: \: \frac{3x - 15}{x - 5} = \frac{3(x - 5)}{x - 5} = 3 \\ [/tex]

[tex]2. \: \: \: \: \: \frac{a}{3} + \frac{1 - 2a}{2} = \frac{2a + 3 - 6a}{6} = \frac{3 - 4a}{6} \\ [/tex]

[tex]3. \: \: \: \: \: \frac{x}{x + y} - \frac{x}{y} = \frac{xy - {x}^{2} - xy }{y(x + y)} = - \frac{ {x}^{2} }{y(x + y)} \\ [/tex]

[tex]4. \: \: \: \: \: \frac{ {b}^{2} - {6a}^{2} }{3a + b} + 3a - b = \frac{ {b}^{2} - {6a}^{2} + {9a}^{2} + 3ab - 3ab - {b}^{2} }{3a + b} = \frac{ {3a}^{2} }{3a + b} [/tex]