Let's see how we can decompose this.

This is the expression we want to decompose or expand.

We can decompose rotation curves to the contributions from different components.

We can use statistics of observed shapes to try to decompose, to project what's going on.

The Infinity Burial Project, an alternative burial system that uses mushrooms to decompose and clean toxins in bodies.

I'm calling body decompiculture and toxin remediation the cultivation of organisms that decompose and clean toxins in bodies.

If those plants die, they decompose, and tiny microorganisms break down those carbohydrates and again, release greenhouse gases as a byproduct.

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

Maybe we could decompose the product that is, take it apart and offer these as add ons or as ancillary products or separate products, etc.

So in this multiple multiple choice quiz, I'd like you to mark each one of these HTML fragments that would decompose into this sequence of five elements.

Un bundling is just a fancy word for saying can I somehow decompose the product into separate pieces, giving some for free or if you're lucky, charging for everyone of them.

The trick was to decompose the computer's construction into numerous stand alone modules, each of which could be individually specified, built and unit tested in isolation from the rest of the project.

One thing I want to point out is that underneath these live epiphytes, as they die and decompose, they actually construct an arboreal soil, both in the temperate zone and in the tropics.

The Infinity Burial Project began a few years ago with a fantasy to create the Infinity Mushroom a new hybrid mushroom that would decompose bodies, clean the toxins and deliver nutrients to plant roots,

Well, anyway, the next step if we really want to decompose this rational expression is to figure out what this part of it is, and the way to do that is with algebraic long division.

The whole idea is to take rational functions and a rational function is just a function or expression where it's one expression divided by another and to essentially expand them or decompose them into simpler parts.

You can decompose those in series of waves overlapping and the matter would fall towards the densest parts and because the matter and radiation are tightly coupled before the microwave background was released, radiation would follow, inducing some slight Doppler shifts in its thermal emission.

The first thing to do with any of these rational expressions that you want to decompose is to just make sure that the numerator is of a lower degree than the denominator, and if it's not, then you just do the algebraic long division like we did in the first video.

And so the answer here and I'll just show you how to do it, I'll maybe leave it to you a little bit to think about why it works is to decompose it almost like this, but instead of having C over x minus 2, you're going to have C over x minus 2 squared.

The next thing to do, if we're going to decompose this into its components, we have to figure out the factors of the denominator right here, so that we can use those factors as the denominators in each of the components, and a third degree polynomial is much, much, much harder to factor than a second degree polynomial, normally.

And we're going to expand it into two simpler expressions where each of these are the denominator and I will make the claim, and if the numbers work out then the claim is true I'll make the claim that I can expand this, or decompose this, into two fractions where the first fraction is just some number a over the first factor, over x plus 5, plus some number b over the second factor, over x minus 8.