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Adding, subtracting and finding the least common multiple

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1/(m+7)-1/(m+3)

This solution deals with adding, subtracting and finding the least common multiple.

Solution found

(-4)/((m+7)*(m+3))
(-4)/((m+7)*(m+3))

Step by Step Solution

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Step  1  :

              1  
 Simplify   —————
            m + 3

Equation at the end of step  1  :

     1         1  
  ——————— -  —————
  (m + 7)    m + 3

Step  2  :

              1  
 Simplify   —————
            m + 7

Equation at the end of step  2  :

    1        1  
  ————— -  —————
  m + 7    m + 3

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       m+7 

      The right denominator is :       m+3 

                  Number of times each Algebraic Factor
            appears in the factorization of:
    Algebraic    
    Factor    
 Left 
 Denominator 
 Right 
 Denominator 
 L.C.M = Max 
 {Left,Right} 
 m+7 101
 m+3 011


      Least Common Multiple:
      (m+7) • (m+3) 

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 = m+3

   Right_M = L.C.M / R_Deno = m+7

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.           m+3     
   ——————————————————  =   —————————————
         L.C.M             (m+7) • (m+3)

   R. Mult. • R. Num.           m+7     
   ——————————————————  =   —————————————
         L.C.M             (m+7) • (m+3)

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:

  m+3 - (m+7)              -4       
 —————————————  =  —————————————————
 (m+7) • (m+3)     (m + 7) • (m + 3)

Final result :

          -4       
  —————————————————
  (m + 7) • (m + 3)

Why learn this

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