We have a b squared over b to the third power

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

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

And all of these are divisible by 5.

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

Times v1 dot v1.

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

No, my brougham is waiting.

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

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

let's cancel that out.

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.

Times negative one.

Minus va minus 400 12.

So what does this simplify to?

So this whole expression simplifies to

And this number is the same as this number.

We have all of that over minus 16.

let's cancel that out.

And then you make some assumptions about it.

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

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

And I'll show you how that's done in a reasonably fair way.

These guys down here cancel out.

You would get 8 minus 4 is 4.

Let me use a slightly different color. We have an a to the ninth. over a squared.

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

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

What's that going to simplify to?

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

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.

And you could leave it this way, or you could actually try to simplify this a little bit.

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

So let's multiply both sides by mu.

We've stated the domain.

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

And let's see what this simplifies to.

We have one expression on top of another expression.

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

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

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

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

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