How do I simplify this expression? {3x}^{ (3)/(2) } - {9x}^{ (1)/(2) } + {6x}^{ ( - 1)/(2) }

Question

How do I simplify this expression?


`{3x}^{ (3)/(2) } - {9x}^{ (1)/(2) } + {6x}^{ ( - 1)/(2) }`

Answer 1

We can write

`3x^(3/2)-9x^(1/2)+6x^(-1/2)=3x^(2-1/2)-9x^(1-1/2)+6x^(-1/2)`

and see that each term has a common factor of
`3x^(-1/2)`; factoring this from each term gives

`3x^(3/2)-9x^(1/2)+6x^(-1/2)=3x^(-1/2)(x^2-3x+2)`

We can factorize this further:

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

This is probably what is meant by "simplify"...