Find LCD and show work

Question

1/6x² + 1/9x²+9x

Answer 1

Find LCD and show work
1/6x² + 1/9x²+9x

 

Let's write the equation as (1/6x²) + (1/9x²) + (9x/1)

 

Do a "prime factorization" of each of the denominators; that is, factor them down to prime numbers:

 

6x² = 3*2*x²

 

9x² = 3*3*x²

 

1 = 1       (we really don't need to do a prime factorization of 1, but I show it here for illustration)

 

The LCD is equal to the product of each unique prime factor.  If a factor appears multiple times, you must include it in the LCD the most times it appears in any prime factorization.  So we see that 3 appears as a prime factor once for 6x² and twice (3*3) for 9x².  Hence the LCD must include 3*3.

 

LCD = 3*3*2*x²*1 = 18x²