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 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).

Hello from MrBillDoesMath!

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

12 servings. 4 times 3= 12