Concept explainers
Does it matter whether you use the LCD first or the GCF first when adding or subtracting a rational expression with different denominators and simplifying? Use an example to justify your claim.
To state if it does matter whether to use the LCD first or the GCF first while adding or subtracting a rational expression with different denominators.
Answer to Problem 16P
If the denominators have no common factors, the LCD is calculated first by simplifying their product.
If the denominators have common factors, the GCF is calculated first and then the LCD is calculated by dividing their product by their GCF.
Explanation of Solution
Given information:
The given statement is:
“Does it matter whether you use the LCD first or the GCF first while adding or subtracting a rational expression with different denominators and simplifying? Use an example to justify your claim.”
If the denominators have no common factors, the LCD is calculated first by simplifying their product.
If the denominators have common factors, the GCF is calculated first and then the LCD is calculated by dividing their product by their GCF.
In the expression
The sum is
In the expression
The sum is
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