# Math Help - Algebra, indices.

1. ## Algebra, indices.

Q= Simplify [ x^(3/2) - x^ (-1/2) ] all of this divided by [ x^(1/2) - x^(-1/2)]

Cheers for the help

2. Originally Posted by sparky69er
Q= Simplify [ x^(3/2) - x^ (-1/2) ] all of this divided by [ x^(1/2) - x^(-1/2)]

Cheers for the help
$\frac{ x^{1,5} - x^{-0,5} }{ x^{0,5} - x^{-0,5} }$

$= \frac{ x^{0,5}(x^{1} - x^{-1}) }{ x^{0,5}(x^{0} - x^{-1}) }$

$= \frac{ x - x^{-1} }{ 1 - x^{-1} }$

$= \frac{ x - x^{-1} }{ 1 - x^{-1} } \times \frac{x}{x}$

$= \frac{ x^2 - x^{0} }{ x - x^{0} }$

$= \frac{ x^2 - 1 }{ x - 1 }$

$= \frac{ (x + 1)(x - 1) }{ (x - 1) }$

$= x + 1$

$
(x \neq 0;1)
$

3. Originally Posted by janvdl
$= x + 1$
Remember to label the domain, $x \neq 0, 1$, else this and the original expression won't be exactly the same.