Similarity and Differences between adding rational expressions and polynomial expressions.

Difference

When polynomials expressions are added, the like terms are evident by mere inspection as the variables need not be further simplified. But with radical expressions, it is a must that the expressions are simplified to figure the like terms.

Simplification is mandatory while adding radical expressions but while adding polynomial expressions; there is not need for further simplification before addition.

In the above example of addition of polynomial expressions, no further simplification was needed prior to group and addition of like terms.

In the above example with adding rational expressions, simplification is a must before proceeding with categorizing like terms and adding them.

Similarity

The similarity between addition of radical expressions and that of addition of polynomial expressions is that same rules are applied for addition in either case, but in radical expressions rules are applied after simplification.

Radical expression area grouped in similar way as terms in polynomial expressions while adding.

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