Maths

√[(a - b)2] must be positive, thus √[(a - b)2] = b - a

√[(a - c)2] must be positive, thus √[(a - c)2] = c - a, i.e. √[(a - c)2]/(a - c) = -1

√[(a - b)2] - |b + c| + |a + c| + √[(a - c)2]/(a - c)

= b - a - |b + c| + |a + c| - 1

There are 3 possibilities:

(I) If b + c < 0 and a + c < 0:

b - a - |b + c| + |a + c| - 1 = b - a + (b + c) - (a + c) - 1 = 2b - 2a - 1

(II) If b + c > 0 and a + c < 0:

b - a - |b + c| + |a + c| - 1 = b - a - (b + c) - (a + c) - 1 = -2c - 2a - 1

(I) If b + c > 0 and a + c > 0:

b - a - |b + c| + |a + c| - 1 = b - a - (b + c) + (a + c) - 1 = - 1