Last week in Pre-Calculus 11 we learned about multiplying and dividing rational expressions. A thing to remember about expressions is that it does not have an equal sign and you do not need to solve, you only need to simplify. I will be teaching you what non-permissible values are and how to determine what they are.

**Non-permissible value** : Values that cause the fraction to have a denominator with a value of zero. (In math, we cannot divide by zero).

Here is an example of multiplying rational expressions

**Steps: **

Non permissible values:

- remove (x-3) from top and bottom because they cancel eachother out
- then it becomes…

**Step 2**: Simplify by multiplying across (Just do it)

**Step 3**: Take the highest common factor from both the numerator and the denominator.

In this case 6 is the highest number that goes into both.

**Step 4**: Notice that x is on the bottom and the top, if it has a pair it can cancel out. two x’s on the bottom one on the top. when they cancel out each other you will be left with only 1 on the bottom.

**Final Answer**:

**Dividing Rational Expressions **

There are many steps when dividing rational expressions

- Simplify the fraction: can factor or take out the common denominator.
- State the non permissible values.
- Reciprocate the second fraction and it will because a multiplication expression.
- State the restrictions again because there are new values in the denominator and could be non-permissible.
- Simplify (cancel out like terms that have a pair on the numerator and denominator.
- Multiply across (Just do it)
- Simplify again if possible.

**Step 1:** Simplify

FACTOR:

**Step 2:** Non-permissible values

**Step 3: **Reciprocate

**Step 4:** Non-permissible values

**Step 5:** Cross out like terms

**Step 6:** Multiply across if possible

- In this example it is not

**Step 7: **Simplify further if possible

- In this example it is not

**Final Answer:**

This is how you Multiply and Divide Rational Expressions