And what do we get?

Well, phi is equal to A over B, which is equal to A plus B over A we know that A plus B over A is the same thing as

And then our denomenator is going to be

A to the fifth literally means a times a times a times a times a.

Here's one regular expression that captures all the ones on the left and none of the ones on the right.

Or the other way, you could imagine, is when you decrease the exponent, what are we doing?

So let's divide by a again, so one over a.

So if we go from a to the first, which is just a, and divide by a, right, so we're just going to go we're just going to divide it by a.

It looks something like that.

And if you think about it, if both of these things are true, then actually not only is A inverse the inverse of A, but

So this'll be a because I just distribute the a, right? a times a to the zero, plus a times a to the 1, plus a times a squared, plus all the way a times a to the n minus one, plus a times a to the n.

left with an a in the numerator, and a divided by a is just 1.

So this term now if we substitute r3 with that, this will just turn into a this will just turn into a plus 1.

A over A plus B over A

So that's another ax.

b squared is 9, so this is going to be the same thing as

What's a to the one? a to the one, we said, was a, and then to get to a squared, what did we do?

Well, this is equal to a times a to the zero.

And then to get to a cubed, what did we do?

And then to get to a to the fourth, what did we do?

So to go from a to the minus one to a to the minus two,

And remember I said 50 minutes was 5 6 of an hour, so the minutes it takes is a, that a, minus this.

So the positive exponents, so you have a to the one, a squared, a cubed, a to the fourth.

Same drill.

And then, 54 minus 5 that is 49, and we're done.

If I do something to one side of the equation, I have to do it to the other.

This is the Laplace transform of e to the and what's a? a is what we shifted by.

So let's say scenario F. Let's call these scenarios.

180 plus 36 is 216.

Plus this a times that a.

If you multiply this out, you have a times a, which is a squared, plus a times negative b, which is negative ab that's a times negative b plus b times a, which is the same thing as ab.

So this is equal to s a times the Laplace transform of sine of a t.

So when x is equal to 1, we get let me pick another color A times, 1 minus 2 is minus 1, squared is just 1.

Well if y is equal to 0, that puts us along the x axis, and you get x squared over a squared is equal to 1, which means that x squared is equal to a squared, which means that x is equal to plus or minus a.

Well the C could be for Cardboard

Now N refers to a value 4, but that doesn't change the value A refers to.

You get x squared is equal to a squared, and then you get x is equal to the plus or minus square root of a.

The second one is always true.

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So this is a to the seventh power. (A to the five plus two power.)

And we show why this works in a previous video.

So let's do that.

Let me do it here.

If we wanted to decompose this partial fraction, or expand it, it would be A over x minus a it's a different a.

So we're going to take a to the zero and divide it by a. a to the zero is one, so what's one divided by a?