Week 15 – Multiplying and dividing rational expressions

This week in pre-calc we learned how to multiply and divide rational expressions together.

You always want to state your non-permissible values first.

For multiplying, the first step to make simplifying your answer easier is to start by reducing your expression with a common factor. Doing this makes multiplying the numbers together a smaller answer and seems better. To reduce with a common factor, you need to use the numerator and find a common factor with a denominator from another expression.

After you’re done reducing your fractions, you can multiply straight across, numerator x numerator and denominator x denominator. Once you’re done that, you can see if you can simplify any more and get the lowest possible fraction.

If you can factor the expression, start by doing that and if you can cancel out terms that are exactly alike, you can make your multiplying easier.

When it comes to dividing, you want to state the non-permissible values of only the terms after the 1st one. After stating those, you want to flip the second fraction and then factor it out. Once you do that you can cancel exact terms and multiply throughout.

It’s important to remember you cannot factor and cancel out terms then flip the second fraction because you will get a completely different answer from the right one.

Week 14 – Adding and subtracting rational expressions and equations

This week in pre-calc, we learned how to add and subtract ration equations and expressions in 4 easy steps.

1. Determine the lowest common denominator (LCD). The lowest common denominator is the number 2 denominators have in common when they’re multiplied. So if 3 and 4 were in the denominator, the lowest common denominator is 12. Its like lowest common multiple. The first number they have in common when multiplied.
2. Rewrite each equation with the LCD in the denominator. When you find the lowest common denominator, you multiple each fraction by the LCD until you get the same denominator for all the fractions. You also need to multiply the numerator as well so you can add or subtract all your numbers over one common denominator.
3. Solve. After rewriting the question, you can simply the whole equation by collecting all your like terms and adding or subtracting them together all under your LCD.
4. Reduce if possible. You can reduce your equation only if it can be reduced on the top and bottom by the same number.

Week 6 – Solving Quadratic Equations

This week in pre-calc, we learned how to solve a quadratic equation by factoring. The equation $ax^2$ + bx + c = 0. A, B, & C are all constant terms and A cannot be equal to 0. When factoring a quadratic equation, you use the zero product property. This means you take your quadratic equation and you start by factoring. Once you’re done factoring, you’ll have 2 terms that should be equal to 0.

Ex. $x^2$ -5x + 6 = 0

(x – 2)(x-3) = 0

Once you factor your equation, you take each term and find out the value of x in order for the term to be equal to 0.

Ex. (x-2) = a (x-3) = b

a=0

b=0

a = (x-2) = 0, x = +2

b = (x-3)=0, x = +3

Basically you’re taking the opposite number to find x in order to make the term equal to 0.

(x – 2)(x-3) = 0

(2-2)(3-3) = 0

(0)(0)=0

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