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 in simplest form, we need to simplify both the numerator and the denominator.
Starting with the numerator:
3x + 18 = 3(x + 6)
Now let's simplify the denominator:
x^2 - 36 = (x - 6)(x + 6)
Now, we can rewrite the expression as:
[3(x + 6) / 4x + 8] ÷ [(x - 6)(x + 6) / x + 2]
To divide by a fraction, we can multiply by its reciprocal. So, the expression becomes:
[3(x + 6) / 4x + 8] * [x + 2 / (x - 6)(x + 6)]
Simplifying the numerator:
3(x + 6) = 3x + 18
Simplifying the denominator:
4x + 8 = 4(x + 2)
(x - 6)(x + 6) remains the same.
Now, the expression becomes:
(3x + 18) / (4x + 8) * (x + 2) / (x - 6)(x + 6)
We can simplify further by canceling the common factors:
1 * (x + 2) / (x + 6)
Final answer: (x + 2) / (x + 6)
Wrong
Apologies for the mistake. Let's correct it:
To express the expression (3x+18)/(4x+8) ÷ (x^2−36)/(x+2) in simplest form, we can simplify each fraction in the numerator and denominator separately.
Numerator: (3x+18)/(4x+8)
We can factor out 3 from both terms in the numerator:
3(x+6)/(4(x+2))
Simplifying further, we get:
3(x+6)/4(x+2)
Denominator: (x^2−36)/(x+2)
The denominator can be factored as the difference of squares:
[(x-6)(x+6)]/(x+2)
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 its reciprocal. So, the expression becomes:
[3(x+6)/4(x+2)] * [(x+2)/(x-6)(x+6)]
Cancelling out common factors, we can simplify it even further:
3/4(x+2)(x-6)
Final answer: 3/4(x+2)(x-6)