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♣ !!!!!!!!!!!