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 ) .

No, she is right

Step-by-step explanation:

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

The (x+3) will cancel

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)