Question

Please help me out I'll give you a virtual high five​

Answer 1

`\red{ \bold{(2x(x - 1) + 3(2x - 3))/((2x + 3)(2x - 3)(x - 1)) }}`

Explanation:

`\frac{2x}{4 {x}^(2) - 9 } + \frac{3}{2 {x}^(2) + x - 3} \\ \\ = \frac{2x}{(2 {x})^(2) - {(3)}^(2) } + \frac{3}{2 {x}^(2) - 2x + 3x - 3} \\ \\ = (2x)/((2x + 3)(2x - 3)) + \frac{3}{2 {x}(x - 1) + 3(x - 1)} \\ \\ = (2x)/((2x + 3)(2x - 3)) + (3)/((x - 1) (2x + 3)) \\ \\ = (2x(x - 1))/((2x + 3)(2x - 3)(x - 1)) + (3(2x - 3))/((x - 1) (2x + 3)(2x - 3)) \\ \\ \purple{ \bold{ = (2x(x - 1) + 3(2x - 3))/((2x + 3)(2x - 3)(x - 1)) }}`