Question

What is the quotient t+3/t+4÷(t²+7t+12)​

Answer 1

The quotient t + 3/t + 4 ÷ (t^2 + 7t + 12) is 1/(t + 4).

Step-by-step explanation:

To find the quotient, we need to divide t + 3/t + 4 by (t^2 + 7t + 12). Here's how we can do it:

Step 1: Factor the denominator:

(t^2 + 7t + 12) can be factored as (t + 4)(t + 3).

Step 2: Rewrite the division as multiplication by the inverse:

Division is the same as multiplication by the inverse. Therefore, we can rewrite the expression as:

(t + 3)/(t + 4) * 1/((t + 4)(t + 3))

Step 3: Simplify the expression:

(t + 3)/(t + 4) * 1/((t + 4)(t + 3)) = (t + 3) * 1 / ((t + 4)(t + 3))

Step 4: Cancel out common factors:

We can cancel out the (t + 3) term in the numerator and denominator:

(t + 3) * 1 / ((t + 4)(t + 3)) = (t + 3) * 1 / (t + 4)(t + 3) = 1 / (t + 4)

Therefore, the quotient of t + 3/t + 4 ÷ (t^2 + 7t + 12) is 1/(t + 4).