What is the first step in factoring the following problem?
(ax + b)^(-1/2) - root {(ax + b)/b}
Seems you'd start by using this rule: a^(-p) = 1 / a^p
1 / (ax + b)^(1/2) - {(ax + b)/b}^(1/2)
Remember that root n = n^(1/2)
Also, if you continued the factoring process, I suggest
setting ax + b = k, to get something simpler to work with:
1 / k^(1/2) - (k/b)^(1/2)
Although k = ax + b in this method, I don't see a direct/handy route for showing a factor being taken out.
Starting over:
(ax + b)^(-1/2) - root {(ax + b)/b}
$(ax + b)^{-1/2} - \dfrac{(ax + b)^{1/2}}{b^{1/2}} =$
$(ax + b)^{-1/2} - (ax + b)^{1/2}b^{-1/2} =$
$(ax + b)^{-1/2}{b^{-1/2}}[b^{1/2} - (ax + b)] = $
$[b(ax + b)]^{-1/2}(b^{1/2} - ax - b)$
After this post, I don't expect to post further on this thread.