For all real numbers $\,A\,$ and $\,B\,$, and for $\,C\ne 0\,$: $$ \frac{A+B}{C} = \frac{A}{C} + \frac{B}{C} \qquad \text{ and } \qquad \frac{AB}{C} = \frac{A}{C}  \frac{B}{C} $$ Key idea: every term in the numerator must be divided by the denominator.
The goal: go immediately from the original expression (like $\displaystyle\,\frac{2t  t^3 + 10t^4}{5t^3}\,$) to the final expression ($\displaystyle\,\frac{2}{5t^2}  \frac{1}{5} + 2t\,$),
without writing down any intermediate step(s).
To do this, use the ‘threepass’ system (sign/size/variable), illustrated next:
$\displaystyle \frac{\class{highlight}{2t}  t^3 + 10t^4}{\class{highlight}{5t^3}}$ 

result: $\displaystyle\frac{\color{green}{2}}{\color{green}{5}\color{blue}{t^2}}$ 
$\displaystyle \frac{2t\class{highlight}{  t^3} + 10t^4}{\class{highlight}{5t^3}}$ 

result: $\displaystyle \color{red}{} \frac{\color{green}{1}}{\color{green}{5}}$ 
$\displaystyle \frac{2t  t^3\class{highlight}{ + 10t^4}}{\class{highlight}{5t^3}}$ 

result: $\displaystyle \color{red}{+}\color{green}{2}\color{blue}{t}$ 
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
