Each step of a simplification process must be justifiable using the properties of algebra.

1. Examine the justification for each step in the simplification below.
   Given expression: $2 ( x + \frac { 3 } { x } ) - \frac { 4 } { x }$
   Step 1: $2 x + \frac { 6 } { x } - \frac { 4 } { x }$ Distributive Property
   Step 2: $\frac { 2 x ^ { 2 } } { x } + \frac { 6 } { x } - \frac { 4 } { x }$Multiplicative Identity (1 · a = a)
   Step 3:$\frac { 1 } { x } ( 2 x ^ { 2 } + 6 - 4 )$ Distributive Property
   Step 4: $\frac { 2 x ^ { 2 } + 6 - 4 } { x }$ Definition of Division ($a \div b = a ( \frac { 1 } { b } )$)
   Step 5: $\frac { 2 x ^ { 2 } + 2 } { x }$ Associative Property of Addition

2. Use the properties of algebra to justify each step in simplifying the expression in part (d) of problem

   Hint:

   The steps will be similar to those in the example. Make sure to give appropriate reasons.