This week in Precalc 11 I learned about adding, subtracting, multiplying, and dividing rational expressions.

For all of these, the main point is to find a common denominator, which can be found by either multiplying the denominators together or finding their lowest common factor.

For multiplication, it’s the most straight forward. You just multiply the terms in the numerator normally.

When it comes to division, you’ll need to flip the second fraction so it can be multiplied instead, and continue like you would with multiplication.

With addition, after finding a common denominator, you add up the numerator as you normally would with common terms.

Finally, with subtraction, once you’ve gotten your common denominator you subtract the common terms like normal.

For any of these, simplify when possible.

This week in Precalc 11 we learned about rational expressions and reducing them. A rational expressions is a fraction of integers, and is the main focus of this unit.

However, they can often include factors or larger terms, and it can be a lot of math to do. In order to avoid this, we have to reduce these fractions to the simplest terms. Yet, it’s not the same as a typical fraction. With normal fractions, we divide the numbers by the same number until they’re as low as possible.

With rational expressions that have large polynomials or factors, we have to start by factoring it if it isn’t. Then, you simply remove pairs of factors if they match, one from the numerator and one from the denominator. Whatever you can’t remove that way is in simplest terms.

This week in Precalc 11 I learned about absolute value functions. Essentially, they start the same as a normal function, however, they cannot have a negative at all.

To start, this means that all negative intercepts are going to be flipped up to be positive, so -7 becomes 7.

Then comes the important part, as the line or parabola will likely hit the x-axis. If this is the case, the line or parabola will have a bounce point, causing it to start heading upwards again. This bounce point can also be found as the x-intercept. It’s always important to keep in mind, as under no circumstances will an absolute value function have negative values.

Additionally, after the bounce point the line or parabola continues normally, simply in the other direction.