find the simplified quotient.\n$\frac{t^{2}-36}{3}div\frac{t^{2}+6t}{9t}$\n$\frac{t - 6}{3}$\n$t - 6$\n$3t +…
find the simplified quotient.\n$\frac{t^{2}-36}{3}div\frac{t^{2}+6t}{9t}$\n$\frac{t - 6}{3}$\n$t - 6$\n$3t + 18$\n$3t - 18$\ndone
Answer
Explanation:
Step1: Rewrite division as multiplication
Dividing by a fraction is multiplying by its reciprocal. So, $\frac{t^{2}-36}{3}\div\frac{t^{2}+6t}{9t}=\frac{t^{2}-36}{3}\times\frac{9t}{t^{2}+6t}$.
Step2: Factor the expressions
Factor $t^{2}-36=(t + 6)(t - 6)$ and $t^{2}+6t=t(t + 6)$. Then the expression becomes $\frac{(t + 6)(t - 6)}{3}\times\frac{9t}{t(t + 6)}$.
Step3: Cancel out common factors
Cancel out the common factors $(t + 6)$ and $t$. We have $\frac{(t - 6)}{3}\times\frac{9}{1}$.
Step4: Simplify the product
$\frac{(t - 6)\times9}{3}=3(t - 6)=3t-18$.
Answer:
$3t - 18$