Answer:
C is the correct option.
Step-by-step explanation:
We have been given the expression
\(\)
When we flip the denominator, the division sign gets changed to multiplication. The rule is shown below
\(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}\)
Using this rule, we have
\(\frac{x^2-5x+6}{15xy^2}\times\frac{5x^2y}{2x^2-7x+3}\)
Now, we can factor the quadratic expressions as
\(x^2-5x+6=x^2-3x-2x+6=(x-3)(x-2)\)
\(2x^2-7x+3=2x^2-6x-x=(x-3)(2x-1)\)
On plugging these values, we get
\(\frac{(x-3)(x-2)}{3\cdot5\cdot xy^2}\times\frac{5x^2y}{(x-3)(2x-1)}\)
On cancelling the common terms in numerator and denominator, we get
\(\frac{x(x-2)}{3y(2x-1)}\)
Hence, C is the correct option.
