Question

Micah was asked to add the following rational expressions:

[Picture 1]

First, he combined like terms in the numerator and kept the common denominator.

[Picture 2]

Next, he simplified the expression by canceling
`x^(2)` because they are “like terms”. His final simplified answer was:

[Picture 3]

Did Micah add the expressions correctly? Explain your answer using complete sentence(s).

Answer 1

Hello from MrBillDoesMath!

Answer: No, the final expression (in the third rectangle) is incorrect.

Discussion.

The simplification shown in the second rectangle is correct but the simplification in the third rectangle (cancelling x^2) is not. The reason is that x^2 does NOT appear in each term in the numerator and denominator in the second rectangle so it can NOT be cancelled.

Now, if the second rectangle contained something like this,

( x^4 + x^3 -4x^2) / (x^4+ 3x^3+ 2x^2)

then x^2 could be cancelled from each term in the numerator and denominator. But that fraction is not what's in rectangle 2 so my original answer stands.

Regard, MrB