Express in simplest form: (3x+18/4x+8) ÷ (x^2−36/x+2)
The possible answers are..
(1/4(x−2)
(4(x−6)/3)
(3/4x−8)
(2/4x−24)
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.
The answer is (2/4x−24)
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.