00:01
Hammy here, let's solve and check this rational equation, shall we? okay, to solve an equation with fractions in it, you can clear the fractions.
00:14
Okay, to clear the fractions basically means undo a fraction.
00:18
A fraction just means you're dividing.
00:22
So if you're dividing, sorry my pen, if you're dividing, the opposite of dividing would be multiplying.
00:28
The opposite of dividing over here would be multiplying.
00:31
However, i could just totally multiply everything through by 3x plus 3 and x squared minus 1.
00:38
That would work.
00:39
But you're going to end up with this huge math problem to solve.
00:43
And it would all come down to the same answer in the end.
00:45
But let's try and keep things a lot more simple.
00:47
So the first thing i'm going to do is i'm going to rewrite this problem and i'm going to factor the denominators.
00:53
So i'm going to rewrite the top would be the same.
00:56
The bottom is a binomial and they have a three in common.
01:01
We call that gcf times what's left.
01:04
That's how you factor it.
01:05
You pull out the gcf, which is the three.
01:08
To get what's left, you divide each term by three.
01:11
3x divided by 3 is x.
01:13
3 divided by 3 is 1.
01:15
So that denominator factors into 3 times x plus 1.
01:21
That's equal to 12 over.
01:24
I'm going to factor this denominator.
01:25
That denominator is difference of squares.
01:30
My little song for that is bino, bino plus n, mino.
01:36
And to get the terms, you just do the square roots of the n.
01:39
So, the square root of x squared is x, the square root of 1 is 1.
01:44
So that denominator factors into x plus 1 times x minus 1.
01:50
Now, basically what i said is we're going to undo the division.
01:56
So let's make a list over here of everything that they're dividing by.
02:00
They're dividing by a 3.
02:02
They're dividing by an x plus 1.
02:04
The second fraction is dividing by an x plus 1 and an x minus 1.
02:10
Yes.
02:12
We need to then multiply by everything they're dividing by.
02:15
So to undo divide by 3, i'm going to multiply by 3.
02:18
To undo divide by x plus 1, i'm going to multiply by x plus 1.
02:23
To undo divide by 1, i'm going to multiply by x by 1.
02:25
To undo divide x minus 1, i'm going to multiply by x minus 1.
02:29
And i kind of repeated myself right here.
02:33
And that's what, again, you can do that.
02:35
It'll work.
02:36
But you're going to make it a lot more work to simplify it down than if you check to see if you actually need two of the same thing.
02:46
And all you do is check each individual denominator.
02:50
This denominator only has one copy of x plus 1.
02:54
This denominator only has one copy of x plus one.
02:57
Therefore, i only need to multiply by one copy of x plus one.
03:02
If any of those denominators had two copies of x plus one, then i would need to multiply by two copies of x plus one.
03:11
But they don't.
03:12
So this is my list.
03:13
This is what i need to multiply everything through by on both sides.
03:18
Because remember the whole keep it balanced.
03:20
You can't do anything to one side unless you do it to the other.
03:23
Golden rule of algebra.
03:24
Do one to this side? you must do one to the other.
03:27
So to undo all of this division, i'm going to multiply both sides by a three by x plus one and by x minus one.
03:37
But i got again, i got to do that to both sides.
03:39
Three times x plus one times x minus one.
03:44
Now to do the math, again, listen to how i read this.
03:48
This says three times x plus one times x minus one times four, divided by 3 divided by x plus 1.
03:58
I'm just going to this is one term.
04:01
I know order of operation says multiply and divide which you guys some some people think means multiply b4 divide.
04:08
No it doesn't not in the same term.
04:10
Okay so i can divide three by three and get one this x plus 1 divided by this x plus 1 is 1.
04:17
So now what i have left is 1 times 1 times 4 times x minus these are all ones now.
04:27
Yes? so i have the ones you don't need to worry when you have multiplication division.
04:32
On the other side, this says three times x plus one times x minus one times 12 divided by x plus one divided by x minus one.
04:44
I'm going to divide first.
04:46
This x plus one divided by this x plus one is one.
04:50
This x minus one divided by this x minus one is one.
04:53
So what's left? is 3 times 12.
04:56
No more fractions.
04:58
We've cleared them.
04:58
We've eliminated them.
05:00
Okay.
05:01
So now if i solve distribute, distribute, i get 4x minus 4 equals 36 and now get x alone.
05:13
I'm going to add 4...