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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}{3x+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.


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