Question

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 ) .

Answer 1

Answer: No, she is right

Step-by-step explanation:

$\frac{2x^2+7x+3}{4x+12}$

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

$\frac{2x(x+3)+(x+3)}{4(x+3)}$

The (x+3) will cancel

$\frac{2x+1}{4}$