Solving Rational Equations

Hi! Today we had two visitors who monitored us in class. Mr. Kuropatwa went over yesterday’s work and also gave us new questions to work on. During the workshop, we has to reach upto 15 slides but we only got to about 9 slides. I will TRY my best to explain everything so you can understand it:)

First, we should all know how to multiply binomials by this time.

For example:

And when its factored it looks like this:

This should all be familiar to us.

When factoring trinomials, you get the ones at the top and when you reverse it you get multiplying binomials. It is like undoing the expressions.

Now Mr. K introduced us an easier and faster way to multiply two digit numbers.

For example:

41 x 31 = ?

First you multiply the two 1st digits

4x3 which equals to 12 then multiply the second digits which are1x1=1

so, so far you have 12 and 1. .leave a blank in between 12__ 1

now to find out what the blank is, you need to do a rainbown multiplication

the rainbow multiplication would be 1x3=3 and 4x1=4 and 3+4 = 7

the middle number would be 7.

The Fast Multiplication relates to the first part because of how the procedures are done.

Heres a picture that might help you understand

Now the second part that we went over is balancing equations.

Ever since i have learned balancing equations form the past, I have

been transposing. .I guess it was the faster way of doing it and easier and I still get the right answer but today in class Mr. K. taught us something new. .

In this type of questions or any questions we DO NOT transpose because we don't just throw numbers from on side to another, we balance it.

to find the x. .

we make zero pairs so since there is x + 3 on the left side and 2 + 3x on the right side.

Add a negative x on the left side and add negative two on the right side.

Right now it isn't balanced so what we do on one side we do on the other

So we need to add -x and -2 on each side to balance the equation--there we go BALANCE EQUATIONS

The next question was. .

First of all find the greatest common factor or GCF. . not LCD because we are dividing to get rid of the denominator.

In this case the gcf is 4 because 4 can be devided by 2 and 4 evenly. When you have found the gcf, you have to multiply it by every term to balance it.

On the first term 4÷2=2 so 2 stays there since it cannot be reduced anymore. Now on the last term, you can reduce 4÷4=1 so it is reduced. REM

EMBER! "REDUCE" not cancell

Now since everything has been reduced you can multiply the rest

Finally. .

The gcf on this equation is x.

However . Make sure to state the restrictions after finding the gfc.

Now multiply x by every term to balance it. On the first term the x's are going to reduce so you're left with a four.

Just multiply every term by x and you will be left with 4= -4x.

To get the x by itself, divide both sides by -4.

JUST REMEMBER DO NOT FORGET TO STATE RESTRICTIONS OR ELSE YOU WILL LOSE A MARK !!!

Mr. K asked us if this was a rational equation, since it can be in fractions it is shown to be rational.

Please feel free to comment on this. Let me know if I have made any errors or if you want to share something and I'll add to it. If you still don't understand, talk to someone who knows best. Thanks and I hope you understand my scribe. .HAPPY HOLIDAYS!!!*

THE NEXT SCRIBE WILL BE ÿâssiÑⁿ♣ !!!!!!!!!!!

Muddiest point

My Muddiest point in pre-cal is understanding analytical geomerty and slopes, word problems. I am also having trouble with that dividing variables (when ms. ingram was our sub).

Where I am. .

Polynomials/Factoring
- this is the unit i know best but still having troubles and making stupid mistakes.

Analytic Geometry
- this unit for me is a little tricky

Trignometry
- this unit is pretty tricky for me as well. . the way the questions were asked . . just needs to understand it better.

Radicals
- radicals for me is confusing sometimes and tricky but now im understading it better, but still needs to learn it more to get a 100% :)

So overall. .
need to learn more and understand it more. .
gotta work harder and pay really close attention.

September 15, 2008

Excercise 9 : Factoring ax² + bx +c

For each question 1 to 5, factor each expression and write "prime" if not factorable.

1. a.) 2x² + 5x + 3
b.) 5x² + 6x + 1

2. a.) 5a² - 16a + 3
b.) 3y² + 4y + 1

3. a.) 24x² + 2x - 1
b.) 6y² + 20 + 23y

4. a.) 10 + y - 2y²
b.) 60y² - 27y - 60

5. a.) 15x² + 37x + 20
b.) 15a² + 8a - 12

6.) Solve for x: 6 - 2 [x - (3 + 4x) } = 8

7.) Solve for x: 4 - x -1 / 2 = x

8.) A square is inscribed in a circle. If the area of the circle is 100pi cm², what is the are of the square?




So this is everything we did in class. .
PLEASE DO ANY HOMEWORK YOU DIDN'T FINISH :)
THANK YOU!!
feel free to comment if I made any mistakes or forgotten anything. .
happy math, bye!


THE NEXT SCRIBE IS JEYSON SACEDA :) !!!