Q= Simplify [ x^(3/2) - x^ (-1/2) ] all of this divided by [ x^(1/2) - x^(-1/2)]
Cheers for the help
$\displaystyle \frac{ x^{1,5} - x^{-0,5} }{ x^{0,5} - x^{-0,5} }$
$\displaystyle = \frac{ x^{0,5}(x^{1} - x^{-1}) }{ x^{0,5}(x^{0} - x^{-1}) }$
$\displaystyle = \frac{ x - x^{-1} }{ 1 - x^{-1} }$
$\displaystyle = \frac{ x - x^{-1} }{ 1 - x^{-1} } \times \frac{x}{x}$
$\displaystyle = \frac{ x^2 - x^{0} }{ x - x^{0} }$
$\displaystyle = \frac{ x^2 - 1 }{ x - 1 }$
$\displaystyle = \frac{ (x + 1)(x - 1) }{ (x - 1) }$
$\displaystyle = x + 1$
$\displaystyle
(x \neq 0;1)
$