60 points been stuck for
perform the indicated operation. what is the numerator in the final expression? type your answer in the space provided. do not include spaces in your answer. if the answer requires an exponent, use the ^ key to indicate the power. for example, if the answer is 2x2y, type 2x^2y.

x over 2 + y over 3 - z over 4

The Numerator is 6x + 4y - 3z

Step-by-step explanation:

Step  1  :

           z

Simplify   —

           4

Equation at the end of step  1  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  2  :

           y

Simplify   —

           3

Equation at the end of step  2  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  3  :

           x

Simplify   —

           2

Equation at the end of step  3  :

  x    y     z

 (— +  —) -  —

  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}  

2101

3011

Product of all  

Prime Factors  236

     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.      y • 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 + y • 2     3x + 2y

—————————————  =  ———————

      6              6    

Equation at the end of step  4  :

 (3x + 2y)    z

 ————————— -  —

     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}  

2122

3101

Product of all  

Prime Factors  6412

     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+2y) • 2

  ——————————————————  =   ———————————

        L.C.M                 12      

  R. Mult. • R. Num.      z • 3

  ——————————————————  =   —————

        L.C.M              12  

Adding fractions that have a common denominator :

5.4       Adding up the two equivalent fractions  

(3x+2y) • 2 - (z • 3)     6x + 4y - 3z

—————————————————————  =  ————————————

         12                    12      

Final result :

 6x + 4y - 3z

 ————————————

      12    

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.