Question P.6.6: Finding the Least Common Denominator Find the LCD of x + 2/2...

Step 1 Factor each denominator completely.

2x – 3 = 1(2x – 3)

x + 3 = 1(x + 3)

Step 2 List the factors of the first denominator.

1, 2x – 3

Step 3 Add any unlisted factors from the second denominator. One factor of the second denominator is already in our list. That factor is 1. However, the other factor, x + 3, is not listed in step 2. We add x + 3 to the list. We have

1, 2x – 3, x + 3.

Step 4 The least common denominator is the product of all factors in the final list. Thus

1(2x – 3)(x + 3)

or (2x – 3)(x + 3) is the least common denominator of \frac{x + 2}{2x – 3} and \frac{4}{x+3}.