Greatest common factor

Question

x^3/2 - x^1/2

 

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

 

(x²+3)^-2/3 + (x²+3)^-5/3

 

Thanks

Answer 1

In each case, the greatest common factor is the SMALLER of the two powers.  Also, remember that x^ax^b = x^a+b.

 

1. x^3/2 - x^1/2 = x^1/2(x - 1)

 

2. (x+3)^1/2 - (x+3)^3/2 = (x+3)^1/2[1 - (x+3)] = (x+3)^1/2(-2 - x)

 

3.  (x² + 3)^-2/3 + (x²+ 3)^-5/3 = (x²+3)^-5/3[(x²+3) + 1]

 

                                         = (x²+3)^-5/3(x²+4)