Melody

It doesn't make sense to me.

it might mean that you are supposed to multiply them together.

The notation is poor, I would interprete according to the rest of the question.   

(2x-1)/(-x+3)>0

It will be positive when the numerator and the denominator are both positive 

so you solve for that.

then

it will also be positive when the numerator and the denominator are both negative so you solve that.

The you include both those answers.  

Take the log of both sides.

You need to know what a log graph looks like.

 $$\\\lim_{x\rightarrow +0}\;\;lnx=-\infty\\
so\\
\lim_{x\rightarrow +1}\;\;ln(x-1)=-\infty\\\\
because \;x-1=0 \;when \;x=1$$

It doesn't make sense to me.

it might mean that you are supposed to multiply them together.

The notation is poor, I would interprete according to the rest of the question.   

$$y=(x+1)^2$$      is a concave up parabola.  The root is x=-1       That is the only value that will make y=0

you want to know where y>0

Well it will be greater than zero everywhere except where x=-1

You should draw the parabola to help you understand why this is so.

Formal solution

$$x \in R \qquad where \quad x \ne-1$$

Not quite.

x could be 38.6

x-22<17

add 22 to both sides

x<39

(2P)^-2 = 1/(2P)^2 = 1/(4P^2)

You need to draw a picture.

The surface of the water will be a horizontal line across the page.

Now the sub is 170m below and the plane is 1800m above the water line.

Now let the picture tell you what must be done     

Thanks Rosala.  

There are a lot of ways to explain this concept.  You gave a good answer  :)