Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            4
 Simplify   —
            5

Equation at the end of step  1  :

   5                 4
  (— • (5x + 9)) +  (— • (1 - 9x))
   3                 5

Step  2  :

Equation at the end of step  2  :

   5                4 • (1 - 9x)
  (— • (5x + 9)) +  ————————————
   3                     5      

Step  3  :

            5
 Simplify   —
            3

Equation at the end of step  3  :

   5                4 • (1 - 9x)
  (— • (5x + 9)) +  ————————————
   3                     5      

Step  4  :

Equation at the end of step  4  :

  5 • (5x + 9)    4 • (1 - 9x)
  ———————————— +  ————————————
       3               5      

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       5 

      Least Common Multiple:
      15 

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 = 5

   Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

 5.3      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.      5 • (5x+9) • 5
   ——————————————————  =   ——————————————
         L.C.M                   15      

   R. Mult. • R. Num.      4 • (1-9x) • 3
   ——————————————————  =   ——————————————
         L.C.M                   15      

Adding fractions that have a common denominator :

 5.4       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:

 5 • (5x+9) • 5 + 4 • (1-9x) • 3     17x + 237
 ———————————————————————————————  =  —————————
               15                       15    

Final result :

  17x + 237
  —————————
     15