Question

What is the simplified form of the quantity 12 z-squared plus 25z plus 12 over the quantity 3 z-squared minus 2z minus 8 ?

4z plus 3 over z plus 2
4z minus 3 over z plus 2
4z plus 3 over z minus 2
4z minus 3 over z minus 2

Answer 1

The simplified form of the expression 12z^2 + 25z + 12 over 3z^2 - 2z - 8 is 4z + 3 over z + 2, after factoring and canceling common terms.

Step-by-step explanation:

To simplify the given rational expression 12z2 + 25z + 12 over 3z2 - 2z - 8, we must factor both the numerator and the denominator, and then reduce the expression by removing common factors.

Factor the numerator: (4z + 3)(3z + 4).

Factor the denominator: (z + 2)(3z - 4).

Cancel out common terms: The (3z - 4) in the numerator cancels with the (3z - 4) in the denominator, yielding 4z + 3 over z + 2.

Therefore, the simplified form of the given expression is 4z + 3 over z + 2.

Answer 2

(12z^2 + 25z + 12)/(3z^2 - 2z - 8) You have to factor it. You know how to factor it right? (12z^2 + 16z + 9z + 12)/(3z^2 - 6z + 4z - 8) (4z(3z + 4) + 3(3z + 4))/(3z(z - 2) + 4(z - 2)) ((4z + 3)(3z + 4))/((3z + 4)(z - 2)) (4z + 3)/(z - 2)