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

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

We need to add the given rational expressions.

First step: Combined like terms in the numerator and kept the common denominator.

`(3x^2-x-9-2x^2+2x+5)/(x^2+3x+2) =(x^2+x-4)/(x^2+3x+2)`

Second step they applied : Canceling the like term x^2 and got
`(x-4)/(3x+2).`

Note: We can't cancel like terms in top and bottom like this.

We can cancel out common factors in top an bottom.

Therefore, Micah did not add the expressions correctly.