How can I solve an equation with two absolute values within a 3rd absolute value?

45 Views Asked by At

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.