Question

Find the simplified quotient t^2-36/3÷t^2+6t/9t

Answer 1

The answer to the question

Answer 2

The simplified quotient is the expression reduced to its simplest term.

The simplified quotient of $\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t}}$ is $\mathbf{3t - 18}$

The expression is given as:

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t}}$

Express as products

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = \frac{t^2 - 36}{3} \times \frac{9t}{t^2 + 6t}}$

Express t^2 as difference of two squares

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = \frac{(t - 6)(t + 6)}{3} \times \frac{9t}{t^2 + 6t}}$

Factor out t from t^2 + 6t

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = \frac{(t - 6)(t + 6)}{3} \times \frac{9t}{t(t + 6)}}$

Delete common factors

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = \frac{t - 6}{3} \times \frac{9t}{t}}$

Delete common factors

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = \frac{t - 6}{3} \times 9}$

Divide 9 by 3

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = t - 6 \times 3}$

So, we have:

$\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t} = 3t - 18}$

Hence, the simplified quotient of $\mathbf{\frac{t^2 - 36}{3} \div \frac{t^2 + 6t}{9t}}$ is $\mathbf{3t - 18}$

Read more about quotients at:

https://brainly.com/question/16134410