That minus two is here and this fourx is here.

Multiply, expressing the product in scientific notation.

We just substituted that for that to get this right here.

Now, we can just multiply both sides of this equation by minus thirteen over three.

Plus two times twox plus two.

And we learned, up here, in this part of the video,

So let's do that.

So we said, oh, well, that means that we're multiplying our original time domain function.

Let's do that.

Let's multiply the top equation I don't know

But what this does is it allows us to get rid of the imaginary part in the denominator.

One times One times four is equal to 4

I'll do it right here.

The reason is we up multiplied each field once for the 0.6 and down multiplied for the 0.2.

I'm still not sure, when there are multiple operations, which one to do first.

So you get equals x squared over a squared plus 1.

And that makes sense because we scaled it by a factor of 2.

It is a three by three matrix.

Subtract y squared from both sides of the equation.

I'm going to give you another presentation on why this works.

Plot them out on complex plane, and see what happens when you multiply them, when you divide them, when you add them, when you subtract them.

So if we assume that x is less than minus 4, then when we multiply both sides of this equation times x plus 4 and you're multiplying it by x minus 3 over x plus 4.

That'll eliminate all of the fractions, so let's do that.

And notice we're getting the exact same value that we got with cross multiplying.

But now we have to make it switched signs like that.

Now if we multiply both sides by x plus 2, x plus 2 is a negative number.

These are just multiple ways of stating the same thing.

Let me switch colors.

But just understand that this is the same thing as this.

OK.

Well, what's that going to be?

That's what we do when we multiply fractions

And when you do it think about the two different ways you could do it.

So let's just do the same step.

And, maybe, the best way to do this, let's multiply both sides of this equation times five four.

This would just jump to 1 by itself.

And i squared is negative one, right?

And what's the partial of this with respect to x?

That's the left hand side.

So dividing by 1 2 is the exact same thing as multiplying by 2 1.

So a1, a2, all the way to an, and they're each going to be multiplied by c.

learned how to graph it.

Try it out.

One definition of exponentiation is that you start with a one, you start with a one, then you multiply this number times a one once.

Notice, when you just multiply something by this, either the 3t and then or either the at, you take the Laplace Transform of it, you just it's the same thing as the Laplace