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My equation is as follows:

Δ = ||(z1 - z2) / r1| - |(z1 - z3) / r2||

where

r1 = sqrt((x1-x2)^2 + (y1-y2)^2)

and

r2 = sqrt((x1-x3)^2 + (y1-y3)^2)

I don't remember much about absolute values, so I did some reading and came up with these formulas:

Δ = (z1 - z2) / r1 - (z1 - z3) / r2

Δ = -((z1 - z2) / r1) - (-((z1 - z3) / r2))

Δ = -((z1 - z2) / r1) - (z1 - z3) / r2

Δ = (z1 - z2) / r1 - (-((z1 - z3) / r2))

-Δ = (z1 - z2) / r1 - (z1 - z3) / r2

-Δ = -((z1 - z2) / r1) - (-((z1 - z3) / r2))

-Δ = -((z1 - z2) / r1) - (z1 - z3) / r2

-Δ = (z1 - z2) / r1 - (-((z1 - z3) / r2))

Is this the correct way to split out my equation or am I completely off? I am trying to figure out the right way to split out the original equation to solve for any values in the variables.

Kyle
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jan 25 '22 at 19:41
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    You should use MathJax! – RedGiant Jan 25 '22 at 19:41
  • Welcome to Math.SE! <> Symbols have no meaning in isolation; it's necessary to say (i) What the notation means (maybe the $z$s are complex, with real and imaginary parts $x$ and $y$?) and (ii) What you mean by solve, i.e., which variable(s) you want to express in terms of others. – Andrew D. Hwang Jan 25 '22 at 21:53

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