Week 16 – Pre-Calc 11

Week 16! We’re getting close to the end of the semester, and that means finals. Putting that aside, right now we are learning about rational expressions and friends with some interesting results.

This week’s big takeaway is the MASSIVE difference between an expression and an equation.

This is always important, but especially in this unit as the questions seem similar… until they aren’t.

Let me give an example.

Let’s say we have this expression:

Step 1: Factor everything as much as possible. It makes life so much easier.

Step 2: Since we have like terms, we can cancel.

Step 3: Since nothing can be reduced further this is our final answer.

Step 4: Identify and non-permissible values

This is basically all you have to do when it comes to a rational expression.

In a rational equation, you are solving for a variable at the end of everything. You know that it is an equation and not an expression because only equations have an equals sign.

Here is an example of a rational equation:

Step 1: Since it is an addition, we must have like terms to add together the fractions. We will also move them to the same side.

Step 2: Now that we have a common denominator, we can add the fractions together.

Step 3: Now since the variable is in the denominator, we can multiply by the denominator to eliminate it. Since we also have to multiply the other side, we end up with the 10f on the other side of the equals sign.

Step 4: From there, we divide to solve for f.

Step 5: Finally, we identify our non-permissible value.

Although similar, it is very important to know the difference between a rational equation and a rational expression.

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