z= 13/2= 6.500
Step-by-step explanation:
Step  1  :
      59
Simplify  ——
      z
Equation at the end of step  1  :
 118   59
 ——— -  ——  = 0
 13   z
Step  2  :
      118
Simplify  ———
      13
Equation at the end of step  2  :
 118   59
 ——— -  ——  = 0
 13   z
Step  3  :
Calculating the Least Common Multiple :
3.1 Â Â Find the Least Common Multiple
   The left denominator is :    13
   The right denominator is :    z
    Number of times each prime factor
    appears in the factorization of:
Prime
Factor  Left
Denominator  Right
Denominator  L.C.M = Max
{Left,Right}
13101
Product of all
Prime Factors  13113
         Number of times each Algebraic Factor
      appears in the factorization of:
  Algebraic  Â
  Factor    Left
Denominator  Right
Denominator  L.C.M = Max
{Left,Right}
z  011
   Least Common Multiple:
   13z
Calculating Multipliers :
3.2 Â Â 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 = z
 Right_M = L.C.M / R_Deno = 13
Making Equivalent Fractions :
3.3 Â Â Â 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.    118 • z
 ——————————————————  =  ———————
    L.C.M        13z Â
 R. Mult. • R. Num.    59 • 13
 ——————————————————  =  ———————
    L.C.M        13z Â
Adding fractions that have a common denominator :
3.4 Â Â Â 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:
118 • z - (59 • 13)   118z - 767
———————————————————  =  ——————————
    13z         13z  Â
Step  4  :
Pulling out like terms :
4.1 Â Â Pull out like factors :
 118z - 767  =  59 • (2z - 13)
Equation at the end of step  4  :
 59 • (2z - 13)
 ——————————————  = 0
   13z   Â
Step  5  :
When a fraction equals zero :
5.1 Â Â When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
 59•(2z-13)
 —————————— • 13z = 0 • 13z
  13z  Â
Now, on the left hand side, the  13z  cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
 59  •  (2z-13)  = 0
Equations which are never true :
5.2 Â Â Â Solve : Â Â 59 Â = Â 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
5.3    Solve  :   2z-13 = 0
Add  13  to both sides of the equation :
           2z = 13
Divide both sides of the equation by 2:
          z = 13/2 = 6.500
One solution was found :
         z = 13/2 = 6.500
