Trying to simplify complex fraction: 1/[1/((x-1) - 2)]

[landgazr]

Argh!

I'm stuck! Well, I guess that goes without saying or I wouldn't be posting.

Although I'm studying pre-calculus right now (implicit domains of composite functions), I am having trouble with an ugly fraction (well, I think so).

I can figure out the composite function with no problem, but they have simplified it to something else and I don't know how they got from this:



to this:



I am sticking with the bottom first, and trying to find a common denominator to subtract from .

I tried using as a common denominator, but I end up getting which doesn't work (unless I messed up there). I know that if you have a fraction as the denominator, you can just multiply by its reciprocal instead. So I am thinking that they figured out how to subtract from then just flipped it, which became the answer because you'd be multiplying by the numerator (1) anyway.

So how did they get from to ?

[stapel_eliz]

I don't know how they got from this: to this:

I am...trying to find a common denominator.... I tried using as a common denominator,
but I end up getting which doesn't work....

What do you mean by this "not working"? (I'm assuming that you typoed the grouping symbols, since there should be parentheses around the "x - 1" when you take the -2 through.)

The steps for the simplification (using the proper grouping symbols for clarity) would be something like:

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

Flip-n-multiply, and you should be good to go!

[landgazr]

Ah! I see what I did wrong.

It was here:



My problem was I didn't add 2; I subtracted it. I messed up a sign. I should have distributed through .

What I meant by it "not working" was that I didn't get from .

I'm not sure I see your point about the grouping symbols, but I do see how you parenthesized , both numerator and denominator, to multiply by to get . Then, since that is its own term, and being subtracted from , I need to make sure that has the correct sign, since subtracting a negative is adding its positive. I know that's very elementary, but it looks like I was on the right track - I just didn't get a sign right.