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Carmella simplified the following rational expression. (2x ^ 2 + 7x + 3)/(4x + 12) = ((2x + 1)(x + 3))/(4(x + 3)) = ((2x + 1)(x + 3))/(4(x + 3)) = (2x + 1)/4 After simplifying the expression , she stated that there are no restrictions on x since the denominator of her answer is a constant and cannot possibly equal Did Carmella make any mistakes in her problem ? If explain and correct her mistake ( s ) .

Sagot :

GeorgePPidn

Answer: No, she is right

Step-by-step explanation:

[tex]\frac{2x^2+7x+3}{4x+12}[/tex]

Factor the trinomial, what two numbers multiply to equal 6 but add to equal 7. That is 6 and 1.

[tex]\frac{2x(x+3)+(x+3)}{4(x+3)}[/tex]

The (x+3) will cancel

[tex]\frac{2x+1}{4}[/tex]

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