what is the quotient?\n$\frac{t + 3}{t + 4}div(t^{2}+7t + 12)$\n$(t + 3)^{2}$\n$(t + 4)^{2}$\n$\frac{1}{(t +…

what is the quotient?\n$\frac{t + 3}{t + 4}div(t^{2}+7t + 12)$\n$(t + 3)^{2}$\n$(t + 4)^{2}$\n$\frac{1}{(t + 4)^{2}}$\n$\frac{1}{(t + 3)^{2}}$

what is the quotient?\n$\frac{t + 3}{t + 4}div(t^{2}+7t + 12)$\n$(t + 3)^{2}$\n$(t + 4)^{2}$\n$\frac{1}{(t + 4)^{2}}$\n$\frac{1}{(t + 3)^{2}}$

Answer

Explanation:

Step1: Rewrite division as multiplication

Dividing by a number is the same as multiplying by its reciprocal. So $\frac{t + 3}{t+4}\div(t^{2}+7t + 12)=\frac{t + 3}{t+4}\times\frac{1}{t^{2}+7t + 12}$.

Step2: Factor the quadratic expression

Factor $t^{2}+7t + 12$. We need two numbers that multiply to $12$ and add up to $7$. The numbers are $3$ and $4$, so $t^{2}+7t + 12=(t + 3)(t+4)$.

Step3: Multiply the fractions

We have $\frac{t + 3}{t+4}\times\frac{1}{(t + 3)(t+4)}=\frac{t + 3}{(t + 3)(t+4)(t+4)}$.

Step4: Simplify the fraction

Cancel out the common factor $(t + 3)$ in the numerator and denominator. We get $\frac{1}{(t + 4)^{2}}$.

Answer:

$\frac{1}{(t + 4)^{2}}$