### Home > A2C > Chapter 6 > Lesson 6.2.3 > Problem6-92

6-92.

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

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