Question

What is the quotient of the rational expression shown below? Make sure your answer is in reduced form.

x^2 +5x+6/ x-6 ÷ x^2-9/3x-12

Answer 1

To find the quotient of the given rational expressions, multiply the first expression by the reciprocal of the second expression.

Step-by-step explanation:

To find the quotient of the given rational expressions, we need to multiply the first expression by the reciprocal of the second expression. The reciprocal of a rational expression is found by flipping the numerator and denominator. So, the reciprocal of x^2-9/3x-12 is 3x-12/x^2-9.

Now, we can multiply the two expressions x^2+5x+6/x-6 and 3x-12/x^2-9. Multiplying the numerators together and denominators together gives:

(x^2+5x+6)(3x-12) / (x-6)(x^2-9)

Then, simplify the expression if possible.