Question

What is the quotient?

StartFraction t + 3 Over t + 4 EndFraction divided by (t squared + 7 t + 12)

Answer 1

The quotient is:

$\frac{1}{(t+4)^2} \text{ or } \frac{1}{t^2+8t+16}$

Solution:

Given expression is:

$\frac{t+3}{\frac{t+4}{t^{2}+7t+12}}$

We have to find the quotient

From given,

$\frac{t+3}{\frac{t+4}{t^{2}+7t+12}} = \frac{t+3}{t+4} \times \frac{1}{(t^2+7t+12)} ------ eqn 1$

$Let\ us\ factor\ (t^2+7t+12)$

Split the middle term

$t^2+7t+12 = t^2 + 3t+4t+12$

Group the terms

$(t^2+3t) + (4t+12)$

Take the common factor out

$t(t+3)+4(t+3)$

Again take (t+3) as common factor

$(t+3)(t+4)$

Substitute in eqn 1

$\frac{t+3}{\frac{t+4}{t^{2}+7t+12}} = \frac{t+3}{t+4} \times \frac{1}{(t+3)(t+4)}$

Cancel the common factors

$\frac{t+3}{\frac{t+4}{t^{2}+7t+12}} = \frac{1}{(t+4)^2}$

Therefore, quotient is:

$\frac{t+3}{\frac{t+4}{t^{2}+7t+12}} = \frac{1}{(t+4)^2} = \frac{1}{t^2+8t+16}$

Answer 2

The quotient of the given expression is $\rm 1/(t+4)^2$ and this can be determined by using the arithmetic operations.

Given :

Expression  --  $\rm \dfrac{t+3}{\dfrac{t+4}{t^2+7t+12}}$

The following steps can be used in order to evaluate the given expression:

Step 1 - The arithmetic operations can be used in order to evaluate the given expression.

Step 2 - Write the given expression.

$\rm \dfrac{t+3}{\dfrac{t+4}{t^2+7t+12}}$

Step 3 - Now, factorize the above expression.

$\rm \dfrac{t+3}{\dfrac{t+4}{t^2+4t+3t+12}}$

$\rm \dfrac{t+3}{\dfrac{t+4}{t(t+4)+3(t+4)}}$

$\rm \dfrac{t+3}{\dfrac{t+4}{(t+4)(t+3)}}$

Step 4 - Simplify the above expression.

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

For more information, refer to the link given below:

https://brainly.com/question/6810544