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Step by step solution :Step  1  : 3 Simplify — 5 Equation at the end of step  1  : 7 9 3 (((—•m)+——)-2m)-— 8 10 5 Step  2  : 9 Simplify —— 10 Equation at the end of step  2  : 7 9 3 (((— • m) + ——) - 2m) - — 8 10 5 Step  3  : 7 Simplify — 8 Equation at the end of step  3  : 7 9 3 (((— • m) + ——) - 2m) - — 8 10 5 Step  4  :Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple 

      The left denominator is :       8 

      The right denominator is :       10 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 23135011 Product of all 
 Prime Factors 81040


      Least Common Multiple: 
      40 

Calculating Multipliers :

 4.2    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 = 4

Making Equivalent Fractions :

 4.3      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. 7m • 5 —————————————————— = —————— L.C.M 40 R. Mult. • R. Num. 9 • 4 —————————————————— = ————— L.C.M 40 Adding fractions that have a common denominator :

 4.4       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:

7m • 5 + 9 • 4 35m + 36 —————————————— = ———————— 40 40 Equation at the end of step  4  : (35m + 36) 3 (—————————— - 2m) - — 40 5 Step  5  :Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction 

Rewrite the whole as a fraction using  40  as the denominator :

2m 2m • 40 2m = —— = ——————— 1 40

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

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions 

(35m+36) - (2m • 40) 36 - 45m ———————————————————— = ———————— 40 40 Equation at the end of step  5  : (36 - 45m) 3 —————————— - — 40 5 Step  6  :Step  7  :Pulling out like terms :

 7.1     Pull out like factors :

   36 - 45m  =   -9 • (5m - 4) 

Calculating the Least Common Multiple :

 7.2    Find the Least Common Multiple 

      The left denominator is :       40 

      The right denominator is :       5 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 23035111 Product of all 
 Prime Factors 40540


      Least Common Multiple: 
      40 

Calculating Multipliers :

 7.3    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 = 8

Making Equivalent Fractions :

 7.4      Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. -9 • (5m-4) —————————————————— = ——————————— L.C.M 40 R. Mult. • R. Num. 3 • 8 —————————————————— = ————— L.C.M 40 Adding fractions that have a common denominator :

 7.5       Adding up the two equivalent fractions 

-9 • (5m-4) - (3 • 8) 12 - 45m ————————————————————— = ———————— 40 40 Step  8  :Pulling out like terms :

 8.1     Pull out like factors :

   12 - 45m  =   -3 • (15m - 4) 

Final result : -3 • (15m - 4) —————————————— 40

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