Question

Anybody knows how to solve this?​

Answer 1

`{ \sf{( (f)/(g) )(x) = \frac{( - {3x}^(2) + 3)}{2x} }} \\ \\ = { \sf{ \frac{( - 3 {x}^(2) + 3)( - 3 {x}^(2) - 3) }{2x( - 3 {x}^(2) - 3) } }} \\ \\ = { \sf{ \frac{( {9x}^(4) + {9x}^(2) - {9x}^(2) - 9) }{ - {6x}^(3) - 6x} }} \\ \\ = { \sf{ (9)/(6)( \frac{ {x}^(4) - 1 }{ - {x}^(3) - x }) }} \\ \\ = { \sf{ - (3)/(2)( \frac{ {x}^(4) - 1 }{x( {x}^(2) - 1)} ) }} \\ \\ = { \sf{ - (3)/(2) ( \frac{( {x}^(2) - 1)( {x}^(2) - 1) }{x( {x}^(2) - 1) }) }} \\ \\ = { \sf{ - (3)/(2)( \frac{ {x}^(2) - 1 }{x} })} \\ \\ = { \boxed{ \sf{ - (3)/(2)(x + (1)/(x) ) }}}`