Answer
[tex]x = 0 \: or \: 4.17 \times {10}^{ - 1} [/tex] ( 5 /12 )
[tex] \frac{3}{2x} - \frac{2}{3x} = 2[/tex]
multiplying the denominators to get the L.C.M since there is no common factor.
[tex]2x \times 3x = 6 {x}^{2} [/tex]
as the L.C .M
so now the general equation becomes
[tex] \frac{ \frac{3}{2x} - \frac{2}{3x} }{6 {x}^{2} } = 2[/tex]
[tex] \frac{9x - 4x}{6 {x}^{2} } = 2[/tex]
[tex]5x = 6 {x}^{2} \times 2[/tex]
[tex]5x = 12 {x}^{2} [/tex]
[tex]12 {x}^{2} - 5x = 0[/tex]
factorizing x
[tex]x(12x - 5) = 0[/tex]
[tex]x = 0[/tex]
[tex]12x - 5 = 0[/tex]
[tex]12x = 5[/tex]
[tex]x = \frac{5}{12} [/tex]
[tex]x = 0.416[/tex]
[tex]x = 4.17 \times {10}^{ - 1} [/tex]
