6x + 8y - 9z  ————————————                 12     Step-by-step explanation:Step  1  :            z Simplify   —            4 Equation at the end of step  1  :   x    y      z  (—+(2•—))-(3•—)   2    3      4 Step  2  :            y Simplify   —            3 Equation at the end of step  2  :   x         y      3Z  (— +  (2 • —)) -  ——   2         3      4  Step  3  :            x Simplify   —            2 Equation at the end of step  3  :   x    2y     3z  (— +  ——) -  ——   2    3      4  Step  4  : Calculating the Least Common Multiple : 4.1    Find the Least Common Multiple      The left denominator is :       2        The right denominator is :       3          Number of times each prime factor        appears in the factorization of: Prime   Factor   Left   Denominator   Right   Denominator   L.C.M = Max   {Left,Right}  2 1 0 1 3 0 1 1 Product of all   Prime Factors  2 3 6      Least Common Multiple:      6   Calculating Multipliers : 4.2    Calculate multipliers for the TWO fractions    Denote the Least Common Multiple by  L.C.M      Denote the Left Multiplier by  Left_M      Denote the Right Multiplier by  Right_M      Denote the Left Deniminator by  L_Deno      Denote the Right Multiplier by  R_Deno     Left_M = L.C.M / L_Deno = 3   Right_M = L.C.M / R_Deno = 2 Making Equivalent Fractions : 4.3      Rewrite the two fractions into equivalent fractions Two fractions are called equivalent if they have the same numeric value. For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well. To calculate equivalent fraction , multiply the NUMERATOR of each fraction, by its respective Multiplier.   L. Mult. • L. Num.      x • 3   ——————————————————  =   —————         L.C.M               6     R. Mult. • R. Num.      2y • 2   ——————————————————  =   ——————         L.C.M               6    Adding fractions that have a common denominator : 4.4       Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: x • 3 + 2y • 2     3x + 4y ——————————————  =  ———————       6               6    Equation at the end of step  4  :  (3x + 4y)    3z  ————————— -  ——      6        4  Step  5  : Calculating the Least Common Multiple : 5.1    Find the Least Common Multiple      The left denominator is :       6        The right denominator is :       4          Number of times each prime factor        appears in the factorization of: Prime   Factor   Left   Denominator   Right   Denominator   L.C.M = Max   {Left,Right}  2 1 2 2 3 1 0 1 Product of all   Prime Factors  6 4 12      Least Common Multiple:      12   Calculating Multipliers : 5.2    Calculate multipliers for the two fractions    Denote the Least Common Multiple by  L.C.M      Denote the Left Multiplier by  Left_M      Denote the Right Multiplier by  Right_M      Denote the Left Deniminator by  L_Deno      Denote the Right Multiplier by  R_Deno     Left_M = L.C.M / L_Deno = 2   Right_M = L.C.M / R_Deno = 3 Making Equivalent Fractions : 5.3      Rewrite the two fractions into equivalent fractions   L. Mult. • L. Num.      (3x+4y) • 2   ——————————————————  =   ———————————         L.C.M                 12         R. Mult. • R. Num.      3z • 3   ——————————————————  =   ——————         L.C.M               12   Adding fractions that have a common denominator : 5.4       Adding up the two equivalent fractions (3x+4y) • 2 - (3z • 3)     6x + 8y - 9z ——————————————————————  =  ————————————           12                    12      Final RESULT :         6x + 8y - 9z  ————————————                  12