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What is the LCD of 1/10x^4 and 4/5x

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2 Answers

1/(10x4) + 4/5x
 
Like any fraction, you can only add or subtract two rational expressions if they have the same denominator.  To find the LCD, you have to do a "prime factorization", factoring each denominator down to its prime numbers.
 
10x4 = 2*5*x4
5x = 5*x
 
The LCD includes each unique prime factor.  If a factor appears in more than one denominator, then choose the factor with the highest power.  So for the above case, the unique prime factors are 2, 5, and x4:
 
LCD = 2*5*x4 = 10x4
 
To add then, we must change the denominator of the second expression to 10x4 by multiplying it by the prime factors of the LCD it is missing, which is 2*x3:
 
1/(10x4) + (4/5x)(2x3/2x3) = 1/(10x4) + (8x3)/(10x4) = (1 + 8x3)/10x4
 
 

Comments

I like your answer! Wendy, Philip is correct.
 LCM of 2 or more numbers with the highest exponents= product of the common factors with highest   exponents  ( 1)
 
  You know that by Fundamental laws of arithmetic every composite number is uniquely equal to the product of its prime factors
 
   Take 2 numbers 36 , 24 ,using statement (1)
      36 = 22 . 32
 
       24 = 23 . 3
   
       LCM ( 24, 36) = 23 . 32 = 8 . ( 9) = 72      ( 2)
 
         If we take   A = a2 b2  , and    B = a3. b
 
        LCM ( A , B ) = a3 b2 , where 36, 24 is a case where a =2 and b=3
 
     Relation (1) implies that lowest number that divides both 36, 24 into it is 72
 
         then
   GCF - greatest Common factor is the greatest factor that both numbers can be divided by it.
             it is the product of the common factor with the lowest exponent.
 
             GCF ( 24, 36) = 4 . 3 = 12
 
              So  :  LCM ( A, B ) = A. B / GCF ( A, B) 
 
               LCM ( 24, 36) = (24 . 36 ) / 12 = 72.  

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