Divide. Express the quotient in simplest form. (x^2+x-12)/(2x)div (x^2-5x+6)/(6x^2) (x-2)/(3x^2)+12x (3x(x^2+x-12))/(x^2)-5x+6 (3x+12)/(-2) (3x^2+12x)/(x-2)

To solve the problem, we need to divide the given expressions and simplify the quotient.Given: First, rewrite the division as multiplication by the reciprocal: Next, factorize the numerators and denominators where possible: Substitute these factorizations back into the expression: Cancel out common factors in the numerator and denominator: Simplify the remaining expression: Cancel out from the numerator and denominator: Simplify the fraction: Thus, the quotient in simplest form is: