Want to 'Solve' a piecewise equation for a common term - comp.soft-sys.math.mathematica

Message from discussion Want to 'Solve' a piecewise equation for a common term

misnomer@gmail.com

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More options 3 Aug 2007, 11:48

Newsgroups: comp.soft-sys.math.mathematica

From: "misno...@gmail.com" <misno...@gmail.com>

Date: Fri, 3 Aug 2007 10:48:49 +0000 (UTC)

Local: Fri 3 Aug 2007 11:48

Subject: Want to 'Solve' a piecewise equation for a common term

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I've been battling to try to get a solution to my equation, but it
requires solving of a piecewise function, which I cannot work out how
to do. Say I have a piecewise function of the form

temp = Piecewise[{
{ 2*N*x, x < 0},
{ N*x, x >= 0}

}]

I want to either solve this via
Solve[1==temp, N]
and either get, with the inequalities,

N -> Piecewise[{
{1/(2*x), x < 0},
{1/x, x >= 0}

}]

or just get mathematica to realise that there is a common term - N,
and factor it out to, say,
N * Piecewise[{
{2*x, x < 0},
{x, x >= 0}

}]

from where solve can handle it perfectly well.

Is this type of operation possible, or am I stuck editing them by hand?

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