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 MultipleÂ
     The left denominator is :       8Â
     The right denominator is :       10Â
        Number of times each prime factor
        appears in the factorization of: PrimeÂ
 Factor  LeftÂ
 Denominator  RightÂ
 Denominator  L.C.M = MaxÂ
 {Left,Right} 23135011 Product of allÂ
 Prime Factors 81040
     Least Common Multiple:Â
      40Â
Calculating Multipliers :
 4.2   Calculate multipliers for the two fractionsÂ
   Denote the Least Common Multiple by  L.C.MÂ
   Denote the Left Multiplier by  Left_MÂ
   Denote the Right Multiplier by  Right_MÂ
   Denote the Left Deniminator by  L_DenoÂ
   Denote the Right Multiplier by  R_DenoÂ
   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.Â
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 fractionsÂ
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 fractionÂ
Rewrite the whole as a fraction using  40  as the denominator :
2m 2m • 40
2m = —— = ———————
1 40
Equivalent fraction :Â The fraction thus generated looks different but has the same value as the wholeÂ
Common denominator :Â 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 fractionsÂ
(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)Â
Calculating the Least Common Multiple :
 7.2   Find the Least Common MultipleÂ
     The left denominator is :       40Â
     The right denominator is :       5Â
        Number of times each prime factor
        appears in the factorization of: PrimeÂ
 Factor  LeftÂ
 Denominator  RightÂ
 Denominator  L.C.M = MaxÂ
 {Left,Right} 23035111 Product of allÂ
 Prime Factors 40540
     Least Common Multiple:Â
      40Â
Calculating Multipliers :
 7.3   Calculate multipliers for the two fractionsÂ
   Denote the Least Common Multiple by  L.C.MÂ
   Denote the Left Multiplier by  Left_MÂ
   Denote the Right Multiplier by  Right_MÂ
   Denote the Left Deniminator by  L_DenoÂ
   Denote the Right Multiplier by  R_DenoÂ
   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 fractionsÂ
-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)Â
Final result : -3 • (15m - 4)
——————————————
40