Final answer:
No, the expression 1/(a+b) is not equal to 1/a + 1/b. The associative property of addition does not apply to fractions or division in the same manner, and a common denominator must be found when adding fractions, which does not split the original expression into two separate fractions.
Step-by-step explanation:
The expression 1/(a+b) is not equal to 1/a + 1/b. This common misconception might arise due to the associative property of addition, which states that A+B=B+A. However, this property does not apply when dealing with the addition of fractions or the division of one number by a sum of numbers.
To understand why these expressions are not equal, consider working with common denominators. For example, to add fractions like 1/2 and 1/3, we need a common denominator, which would be 6 in this case. We transform the fractions to have the same denominator, resulting in 3/6 + 2/6, which can be added to get 5/6. Clearly, simply adding the numerators 1+1 without adjusting the denominators would not yield the correct answer.
Similarly, when dealing with the expression 1/(a+b), we cannot separate it into two fractions without finding a proper common denominator, which in this case, does not lead to 1/a + 1/b.
To correctly manipulate the original expression, we would need to find a common denominator which involves the product of 'a' and 'b', but since 'a+b' is neither 'a' nor 'b', we cannot simply add the fractions as 1/a + 1/b.