Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a1"   was replaced by   "a^1". 

(2): "1.5" was replaced by "(15/10)".

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

                                       3
  (((tg -  (a1250)) -  150) -  150) -  —
                                       2

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

                          -a1250 + tg - 300      (-a1250 + tg - 300) • 2 
     -a1250 + tg - 300 =  —————————————————  =  ———————————————————————
                                  1                        2           

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -a¹²⁵⁰ + tg - 300  =   -1 • (a¹²⁵⁰ - tg + 300) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    a¹²⁵⁰ - tg + 300 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Adding fractions that have a common denominator :

 3.3       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:

 (-a1250+tg-300) • 2 - (3)      -2a1250 + 2tg - 603 
 —————————————————————————  =  ———————————————————
             2                          2         

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -2a¹²⁵⁰ + 2tg - 603  =   -1 • (2a¹²⁵⁰ - 2tg + 603) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    2a¹²⁵⁰ - 2tg + 603 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

  +2a1250 + 2tg + 603 
  ———————————————————
           2