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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.

Respuesta :

Given expression: [tex]\frac{3x^2-x-9}{x^2+3x+2}+\frac{-2x^2+2x+5}{x^2+3x+2}[/tex]

We need to add the given rational expressions.

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

[tex]\frac{3x^2-x-9-2x^2+2x+5}{x^2+3x+2} =\frac{x^2+x-4}{x^2+3x+2}[/tex]

Second step they applied : Canceling the like term x^2 and got [tex]\frac{x-4}{x+2}[/tex].

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.