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 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
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
z 011
Least Common Multiple:
13z
Calculating Multipliers :
3.2 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 = z
Right_M = L.C.M / R_Deno = 13
Making Equivalent Fractions :
3.3 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. 118 • z
—————————————————— = ———————
L.C.M 13z
R. Mult. • R. Num. 59 • 13
—————————————————— = ———————
L.C.M 13z
Adding fractions that have a common denominator :
3.4 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:
118 • z - (59 • 13) 118z - 767
——————————————————— = ——————————
13z 13z
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
118z - 767 = 59 • (2z - 13)
Equation at the end of step 4 :
59 • (2z - 13)
—————————————— = 0
13z
Step 5 :
When a fraction equals zero :
5.1 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
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 Solve : 59 = 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
