Question

See attachment the problem can be found in there

Answer 1

`\frac{ - 2 {x}^(2) + 19x + 3 }{3 {x} (4x^(2) - 9 )}`

Explanation:

`\frac{5}{6 {x}^(2) + 9x} + (1)/(2x - 3) - (2)/(3x) \\ \\ = \frac{5}{3x(2 {x} + 3)} + (1)/(2x - 3) - (2)/(3x) \\ \\ = \frac{5(2x - 3) + 1 * 3x(2x + 3)}{3x(2 {x} + 3)(2x - 3)} - (2)/(3x) \\ \\ = \frac{10x - 15 + 6 {x}^(2) + 9x}{3x((2 {x} ) ^(2) - {3}^(2) )} - (2)/(3x) \\ \\ = \frac{6 {x}^(2) + 19x - 15}{3x(4x^(2) - 9 )} - (2)/(3x) \\ \\ = \frac{3x(6 {x}^(2) + 19x - 15) - 2 * 3x(4x^(2) - 9 )}{3x(4x^(2) - 9 ) * 3x} \\ \\ = \frac{18{x}^(3) + 57 {x}^(2) - 45x - 24x^(3) + 54x }{3x(4x^(2) - 9 ) * 3x} \\ \\ = \frac{ - 6 {x}^(3) + 57 {x}^(2) + 9x }{9 {x}^(2) (4x^(2) - 9 )} \\ \\ = \frac{ 3x(- 2 {x}^(2) + 19x + 3) }{9 {x}^(2) (4x^(2) - 9 )} \\ \\ \huge \orange{ \boxed{= \frac{ - 2 {x}^(2) + 19x + 3 }{3 {x} (4x^(2) - 9 )} }}`