And all of these are divisible by 5.

So let's multiply both sides by mu.

And then you make some assumptions about it.

let's cancel that out.

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

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

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

You would get 8 minus 4 is 4.

So what does this simplify to?

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

Times v1 dot v1.

And this number is the same as this number.

We have all of that over minus 16.

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

We have one expression on top of another expression.

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

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

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

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

And let's see what this simplifies to.

What's that going to simplify to?

Minus va minus 400 12.

So this whole expression simplifies to

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.

So we can do this in multiple ways, simplify different parts.

So we can write this as x plus 2 times x plus 8.

let's cancel that out.

We have a b squared over b to the third power

It's just making sure we're multiplying every part of this number, times every part of that number.

Times negative one.

This is where we just get our algebra hat on, and try to simplify until it's a separable equation in v.

Remember, this thing is just this thing right here, we're just doing the Pythagorean theorem.

Marketing people have never been able to do that.

So it's very valuable to have this mathematical, rigorous, thinking.

We have 7 times 10 to the fifth over 2 times 10 to the negative 2 times 2.5 times 10 to the ninth.

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

So 4 9 is the exact same thing as 16 36.

Another one where they're trying to get the simplest form.

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

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