Express in simplest form: (3x+18/4x+8) ÷ (x^2−36/x+2)

Question

The possible answers are..
(1/4(x−2)

(4(x−6)/3)

(3/4x−8)

(2/4x−24)

Answer 1

To express the given expression in simplest form, we need to simplify both the numerator and the denominator, and then divide them.

First, let's simplify the numerator:
3x + 18 = 3(x + 6)
So the numerator becomes 3(x + 6).

Now, let's simplify the denominator:
x^2 - 36 = (x - 6)(x + 6)

Thus, the denominator becomes (x - 6)(x + 6).

Now we can rewrite the expression as:
(3(x + 6)/(x - 6)(x + 6)) ÷ (x + 2)

Since division is the same as multiplying by the reciprocal, we can rewrite the expression as:
(3(x + 6)/(x - 6)(x + 6)) * (1/(x + 2))

Now, we can multiply the numerators and denominators:
(3(x + 6))/(x - 6)(x + 6)(x + 2)

So the simplified form of the expression is (3(x + 6))/(x - 6)(x + 6)(x + 2).

None of the given options match this simplified form, so none of the possible answers are correct.

Answer 2

The answer is (2/4x−24)

Answer 3

Apologies for the confusion. Let's simplify further:

Starting with the numerator:
3x + 18 = 3(x + 6)

Simplifying the denominator:
x^2 - 36 = (x - 6)(x + 6)

Now the expression can be written as:
(3(x + 6))/((x - 6)(x + 6)) ÷ (x + 2)

Since division is the same as multiplying by the reciprocal:
(3(x + 6))/((x - 6)(x + 6)) * (1/(x + 2))

Multiplying the numerators and denominators:
(3(x + 6))/(x - 6)(x + 6)(x + 2)

Simplifying the numerator:
3(x + 6) = 3x + 18

Thus, the simplified form of the expression is:
(3x + 18)/((x - 6)(x + 6)(x + 2))

Therefore, the possible answer (2/4x-24) is incorrect as it does not match the simplified form of the expression.