Adding, subtracting and finding the least common multiple

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

Solution found

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

See steps

Step by Step Solution

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	1	0	1
m+3	0	1	1

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)