Aim: How do we divide radicals?

When dividing radical expressions, as long as the roots are the same, we can divide the radicals using the following property. You can divide the radicala first or simplify first then divide. Either way you choose to work the problems the results will be the same.
 http://infinity.cos.edu/algebra/ProblemsSolved/Chapter%2009/Chapter%209.4_Multiplication%20and%20Division%20of%20Radicals.pdf

Aim: How do we multiply and divide radical expressions?

The way we multiply and divide radical expressions is by compining the factor and radical together. Then simplifying the radical when multiplying. When dividing a radical you do the same with multplying but then simplfy the radicals.

Aim: How do we simplify radicals?

The way we can simply radicals is finding the multipls of the factor and taking out any pairs of numbers outside of the radical.
Example:

     The radical 52 has the factors of 2x2x13 which equal 52. Since 2 has a pair of 2 which makes 4, you bring the 2^2 out of the radical and leave 13 inside the radical. Since the square root of 2 is 2, you take out the power of 2 and leave it as is for the final answer.

Aim: How do we solve quadratic equations by factoring?

When the product of two factors are equal to zero, at least one of the two factors must equal zero
Example:
   If 10(x+17)=0, then 10 or x+17 must be zero
     x+17=0
     x=-17
  If (x+9)(x-13)=0, then x+17 or x-13 must equal to zero
     x+9=0, x=-9
     x-13=0, x=13

Aim: How do we solve rational proportions?

How you solve rational proportions is by cross multiplying two fractions that are equal to each other to find the value of a variable. After cross multiplying the two fractions, your left with two numbers equaling each other, you then divide the number with the variable to both sides to find with the variable is equal to. 

Aim: How do we add and subtract rational expressions?

The way you add and subtract rational expressions is by trying to get all the denominators of the fractions to be the same. Then cancel out all the denominators when they're the same and solve the equation for the variable that's missing.