Factoring question.

I'm in Pre-Calc so don't bust my balls. I know the factoring stuff is easy but it's like 1:30 AM and this specific problem is bugging me. LULZ EXCUSES

Factoring with fractions as exponents.

x^(-3/2) + 2x^(-1/2) + x^(1/2)


The answer I got was x^-1/2(x+1)^2 but apparently the answer is x^-3/2(x+1)^2 ... I'm normally good at factoring, but the fractions are throwing me off for some reason (don't want to use the time as an excuse, I'm fully functioning, just don't like this stuff.)

Any help? I know it's simple and a breeze for most of you... So if you could help out it'd be great.

For the first one, put x^1/2 in front of everything and you get: x^1/2 * (x^2-1), then you have that (a²-b²) = (a+b)(a-b) which gets you your answer.

For the second one you put the lowest power of X in front (in this case -3/2) so all the others will be positive and easy to work with. After that it's just basic reverse transforming of squares of (a+b) and you'll get there.

They all have x (and only x), so you could just factor anything out. But yes, normally, you wouldn't want to deal with negative and/or factional exponents, so try to put it out in front whenever you can, and choose the most complicated one among them.



When you get used to analyzing stuff at a glance, you'll see that ^(1/2) is one exponent higher than ^(-1/2) which is in turn 1 exponent higher than ^(-3/2), suggesting the form (ax^2 + bx + c).