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 expression (3x+18/4x+8) ÷ (x^2−36/x+2) in simplest form, we first need to simplify the numerator and denominator separately.
Numerator:
3x+18 = 3(x+6)
Denominator:
x^2−36 = (x+6)(x-6)
Now, we can rewrite the expression as:
(3(x+6)/4(x+2)) ÷ ((x+6)(x-6)/(x+2))
To divide by a fraction, we can multiply by the reciprocal. Therefore, the expression becomes:
(3(x+6)/4(x+2)) * ((x+2)/(x+6)(x-6))
Cancel out common factors:
(3/(4(x-6)))
So, the simplified expression is (3/(4(x-6)).
None of the given possible answers matches the simplified form.
Wrong the answer is (2÷4x−24)
Apologies for the mistake. Let's re-evaluate the expression to ensure accuracy.
Given expression: (3x+18)/(4x+8) ÷ (x^2−36)/(x+2)
To simplify this expression, we can rewrite it as:
(3(x+6))/(4(x+2)) ÷ ((x+6)(x-6))/(x+2)
Next, we can flip the second fraction and change the division to multiplication:
(3(x+6))/(4(x+2)) * (x+2)/((x+6)(x-6))
Now, let's cancel out common factors:
(3/4) * 1/(x-6)
Finally, we can simplify the expression to:
3/(4(x-6))
So, the simplest form of the expression is 3/(4(x-6)). None of the given possible answers (2÷4x−24) match the simplified form.
Wrong. The only possible answer is (2÷4x−24)
Apologies for the confusion. Let's re-evaluate the expression correctly.
Given expression: (3x+18)/(4x+8) ÷ (x^2−36)/(x+2)
To simplify this expression, we can rewrite it as:
(3(x+6))/(4(x+2)) ÷ ((x+6)(x-6))/(x+2)
Next, we can flip the second fraction and change the division to multiplication:
(3(x+6))/(4(x+2)) * (x+2)/((x+6)(x-6))
Now, let's cancel out common factors:
3/4 * 1/(x-6)
Finally, we can simplify the expression to:
3/(4(x-6))
I apologize, but this simplified expression does not match the given possible answers.