Question

Micah was asked to add the following expressions:

Answer 1

Given expression: $\frac{3x^2-x-9}{x^2+3x+2}+\frac{-2x^2+2x+5}{x^2+3x+2}$

We need to add the given rational expressions.

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

$\frac{3x^2-x-9-2x^2+2x+5}{x^2+3x+2} =\frac{x^2+x-4}{x^2+3x+2}$

Second step they applied : Canceling the like term x^2 and got $\frac{x-4}{3x+2}.$

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.