Question

Micah was asked to add the following expressions: 3x2−x−9x2+3x+2+−2x2+2x+5x2+3x+2 First, he combined like terms in the numerator and kept the common denominator. x2+x−4x2+3x+2 Next, he simplified the expression by canceling the like term, x2. His final, simplified answer was: x−43x+2 Did Micah add the expressions correctly? Explain your answer using complete sentences.

Answer 1

Micah was asked to add the following expressions:

`(3x^2-x-9)/(x^2+3x+2) + (-2x^2+2x+5)/(x^2+3x+2)`

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

First step is correct. He added the like terms in the numerator, because the denominators are same.

`3x^2 -x -9 -2x^2+2x+5 becomes x^2 +x -4`

So he got ,
`(x^2+x-4)/(x^2+3x+2)`

In the next step, he cannot cancel out x^2 from the top and bottom . Because x-4 and 3x+2 are added with x^2

If we have x^2 is multiplied with other terms at the top and bottom , then we can cancel out x^2.

So Micah added the expression incorrectly. Final answer is not correct.