x^5/2-x^1/2=

Question

x^5/2-x^1/2=

cruffo · Answer

$$x^{1/2} (x^2-1)$$
$$=\sqrt{x}\;(x+1)\;(x-1)$$

anonymous · Answer

I dont get this at all I am sorry I am really bad at this I have failed this 3 times could you do it step by step if you dont mind

anonymous · Answer

or tell me where i can go to do that

cruffo · Answer

Are the instructions "factor" or "simplify" or "solve"

anonymous · Answer

factor compleatley and simplify

anonymous · Answer

completely

cruffo · Answer

:)

anonymous · Answer

I have been up for 20 hours tring to get this

cruffo · Answer

Well, sleep really helps!

So you need to identify the greatest common factor.  When it comes to exponents, this will be the smallest exponent.  In this problem the smaller of the two exponents, either 5/2 or 1/2, is 1/2.

cruffo · Answer

Factoring is like dividing, but we keep the term we divide by on the outside of the parentheses.  So if we factor out x^1/2, we will have
$$x^{1/2} ( ?\quad+\quad ?)$$
Now on the inside of the parentheses...
The first question mark will be 
$$\frac{x^{5/2}}{x^{1/2}} = x^{5/2-1/2} = x^{4/2} = x^2$$

cruffo · Answer

so far ok???

anonymous · Answer

the whole thing? then mult

cruffo · Answer

What we have so far is 
$$x^{1/2}(x^2 + \quad ?)$$
Can you tell me what the remaining "?" should be, and why?

anonymous · Answer

ok

anonymous · Answer

i will try

anonymous · Answer

1 because u have already cancelled out/

cruffo · Answer

great!  That's right,
$$\frac{x^{1/2}}{x^{1/2}} = 1$$
So now we have 
$$x^{1/2}(x^2 - 1)$$
Notice that  x^2 -1 is a difference of squares, so it can be factored further.

anonymous · Answer

I cant believe I got that right

anonymous · Answer

(x-1)(x+1)

cruffo · Answer

Good! So all together,
$$x^{1/2}(x-1)(x+1)$$
Now, some books/teachers will leave the answer as above, and some will write any remaining rational exponents as roots.  x to the half power is the same as the square root of x, so another form of the answer is
$$\sqrt{x}\;(x-1)\;(x+1)$$

anonymous · Answer

o my i think i might have to retake this over makes me sad i have been working on this work sheet for a long time and still  have 4 more ? but thanks a lot wish I would have know about this site sooner

cruffo · Answer

I've been looking around for some good references for this material, but I haven't found much.  May want to check YouTube, search for 
* rational exponents
* factoring with rational exponents

anonymous · Answer

i will do that