Question

1/b+x=3b/2x^2 - 1/x
btw ^2 means square

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Answer 1

`x = ( - 3b)/(4) \: or \: b`

Explanation:

`(1)/(b + x) = \frac{3b}{2 {x}^(2) } - (1)/(x)`

`= > (1)/(b + x) = \frac{3b - 2x}{2 {x}^(2) }`

`= > 2 {x}^(2) = (b + x)(3b - 2x)`

`= > 2 {x}^(2) = 3 {b}^(2) - 2bx + 3bx - 2 {x}^(2)`

`= > 2 {b}^(2) = 3 {b}^(2) + bx - 2 {x}^(2)`

`= > 3 {b}^(2) + bx - 4 {x}^(2) = 0`

`= > 3 {b}^(2) + 4bx - 3bx - 4 {x}^(2) = 0`

`= > b(3b + 4x) - x(3b + 4x) = 0`

`= > (3b + 4x)(b - x) = 0`

Hence,

`x = ( - 3b)/(4) \: or \: b`