SOLUTION: Please help me solve this equation: Directions: tell whether the statement is always true, sometimes true, or never true. Explain your reasoning. Problem: The LCD of two rat

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Question 189079: Please help me solve this equation:
Directions: tell whether the statement is always true, sometimes true, or never true. Explain your reasoning.
Problem:
The LCD of two rational expressions is the product of the denominators.
Thanks! =)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at some examples:

Ex 1: LCD of 1%2Fx and 1%2F%282x%29 is 2x. Also, the product of the denominators is x%2A%282x%29=2x%5E2. So in this case, statement is NOT true. So it CANNOT be always true (all it takes is one counter example). So the statement is either sometimes true or never true.


Ex 2: LCD of y%2F%283z%29 and r%5E2%2F%287w%29 is 21wz. Since %283z%29%287w%29=21wz is the LCD, this shows us that in this case, the statement is true. So this means that we've eliminated the "never true" possibility (as at least one case is true)


So the statement

"The LCD of two rational expressions is the product of the denominators. "

is sometimes true.


Note: the statement is only true if the GCF (or GCD) of the denominators is equal to 1, but we don't have to worry about that technicality.