Answer:
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]
Option C is the correct option
Step-by-step explanation:
[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} [/tex]
To divide by a fraction, multiply by the reciprocal of that fraction
[tex] \frac{x}{3x - 1} \times \frac{2x}{x - 2} [/tex]
Multiply the fractions
[tex] \frac{2 {x}^{2} }{(3x - 1)(x - 2)} [/tex]
Multiply the parentheses
[tex] \frac{2 {x}^{2} }{3x(x - 2) - 1(x - 2)} [/tex]
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 6x - x + 2 } [/tex]
Collect like terms
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]
Hope this helps...
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