Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)". 1 more similar replacement(s)

(2): "1.2" was replaced by "(12/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  1  :

   12               
  (—— • (10-2)) -  (5 • ((2)(-1)•(5)(-1)))
   10               

Step  2  :

Raising to a Power :

 2.1      Canceling out  5  as it appears on both sides of the fraction line

Equation at the end of step  2  :

   12              1
  (—— • (10-2)) -  —
   10              2

Step  3  :

 3.1     10 = 2•5

(10)^-2 = (2•5)^(-2) = (2)^(-2) • (5)^(-2)

Equation at the end of step  3  :

   12                         1
  (—— • ((2)(-2)•(5)(-2))) -  —
   10                         2

Step  4  :

            6
 Simplify   —
            5

Equation at the end of step  4  :

   6                         1
  (— • ((2)(-2)•(5)(-2))) -  —
   5                         2

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Dividing exponents :

 5.2    2¹   divided by   2²   = 2^{(1 - 2)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  5  :

   3     1
  ——— -  —
  250    2

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       250 

      The right denominator is :       2 

      Least Common Multiple:
      250 

Calculating Multipliers :

 6.2    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 = 1

   Right_M = L.C.M / R_Deno = 125

Making Equivalent Fractions :

 6.3      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.       3 
   ——————————————————  =   ———
         L.C.M             250

   R. Mult. • R. Num.      125
   ——————————————————  =   ———
         L.C.M             250

Adding fractions that have a common denominator :

 6.4       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:

 3 - (125)     -61
 —————————  =  ———
    250        125

Final result :

  -61            
  ——— = -0.48800 
  125