Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x1"   was replaced by   "x^1". 

Step  1  :

             x
 Simplify   ——
            10

Equation at the end of step  1  :

   8           x
  (— • x) -  (—— • x)
   9          10
 Step  2  :
            8
 Simplify   —
            9

Equation at the end of step  2  :

   8         x2
  (— • x) -  ——
   9         10

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       9 

      The right denominator is :       10 

      Least Common Multiple:
      90 

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 = 10

   Right_M = L.C.M / R_Deno = 9

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.      8x • 10
   ——————————————————  =   ———————
         L.C.M               90   

   R. Mult. • R. Num.      x2 • 9
   ——————————————————  =   ——————
         L.C.M               90  

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:

 8x • 10 - (x2 • 9)     80x - 9x2
 ——————————————————  =  —————————
         90                90    

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   80x - 9x²  =   -x • (9x - 80) 

Final result :

  +x • (9x + 80)
  ——————————————
        90