If x = -4/9, y = 5/12 and z = 7/18, find the value of

x ÷ y − [ (1 / xy) − y ( (2x / y) ÷ (x / 2y) ) − xyz ( (1 / x) + (1 / y) + (1 / z) ) ].

Using BODMAS rule, we have

The image shows a detailed algebraic simplification and substitution process for the expression:

x ÷ y − [ (1 / xy) − y( (2x / y) ÷ (x / 2y) ) − xyz( (yz + zx + xy) / xyz ) ]

Step-by-step simplification:

= x÷y − [(1/xy) − y(4) − (yz + zx + xy)]

= x÷y − [(1/xy) − 4y − yz − zx − xy]

= x÷y − (1/xy) + 4y + yz + zx + xy

= (x/y) − (1/xy) + 4y + yz + zx + xy

Substituting the given values:

x = -4/9, y = 5/12, z = 7/18

= (-4/9) ÷ (5/12) − 1 / [(-4/9) × (5/12)] + 4 × (5/12) + (5/12 × 7/18) + (7/18 × -4/9) + (-4/9 × 5/12)

= (-4/9 × 12/5) − 1 / (-5/27) + 5/3 + 35/216 − 14/81 + 5/27

This image demonstrates a complete algebraic evaluation involving fractional substitution and simplification.