Answer:
[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]
Step-by-step explanation:
[tex] \frac{1}{b + x} = \frac{3b}{2 {x}^{2} } - \frac{1}{x} [/tex]
[tex] = > \frac{1}{b + x} = \frac{3b - 2x}{2 {x}^{2} } [/tex]
[tex] = > 2 {x}^{2} = (b + x)(3b - 2x)[/tex]
[tex] = > 2 {x}^{2} = 3 {b}^{2} - 2bx + 3bx - 2 {x}^{2} [/tex]
[tex] = > 2 {b}^{2} = 3 {b}^{2} + bx - 2 {x}^{2} [/tex]
[tex] = > 3 {b}^{2} + bx - 4 {x}^{2} = 0[/tex]
[tex] = > 3 {b}^{2} + 4bx - 3bx - 4 {x}^{2} = 0[/tex]
[tex] = > b(3b + 4x) - x(3b + 4x) = 0[/tex]
[tex] = > (3b + 4x)(b - x) = 0[/tex]
Hence,
[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]
