And that can also be written as and this is my preferred notation, because it doesn't have all this extra junk everywhere.

And this number is the same as this number.

let's cancel that out.

So what does this simplify to?

And all of these are divisible by 5.

So let's multiply both sides by mu.

Times negative one.

The length is given right over there it is a squared plus 6 a minus 27 they want us to simplify this.

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

And then you make some assumptions about it.

These will make this expression undefined. It will make this denominator equal to 0.

And let's see what this simplifies to.

So let's factor out a 6. And then 12x divided by 6 is 2x. And then 30 divided by 6 is 5.

I'm starting to see the light at the end of the tunnel.

let's cancel that out.

25i 2 is the same thing as 25 times 1, so that is 25.

You would get 8 minus 4 is 4.

So we start with 5x 2(7x 1) 14x

The trick here is to factor it and simplify it before you do any multiplication.

6 plus 2 is 8.

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Times v1 dot v1.

We have all of that over minus 16.

So this whole expression simplifies to

Is given right up here, is 2x times the principal square root of 5 minus 4, minus 4.

I think we're almost there.

So this is going to be equal to, if we distribute onto that, we get. Minus 2x times the principle square root of 5. Negative 1 times negative 4, is plus or positive 5, and now we can simplify.

We have one expression on top of another expression.

Well, a is minus 10, so 2 times a is minus 20.

We have a b squared over b to the third power

You could bring the 13 down here if you want to write it so you don't have a fraction over a fraction.

What's that going to simplify to?

Minus va minus 400 12.

So this might involve another integration by parts, and it does.

Now, this is actually the hardest part with the quadratic equation is oftentimes just simplifying this expression.

So this is going to be 25, times x to the third.

We could divide both sides of this by 4.

Because if we just simplify this expression, and we include things in the simplified domain that weren't included in the original function's domain, we've actually changed the expression.

All we did is wherever we saw an x, we substituted it, minus 2 there.

But because this is an equation, it equals 0, let's just divide everything by 9.

We've stated the domain.

The numerator has the same degree as the denominator.

This is essentially a way of keeping the gold here and we just use these checking accounts and these bank notes as a way of transacting instead of the gold itself.

That comes from algebra.