Divide.
-$$\frac { x ^ { 2 } + 8 x + 12 } { x + 2 } \div \frac { x ^ { 2 } - 36 } { 2 x - 12 }$$
A) 2
B) $\frac { 1 } { 2 }$

C) $\frac { 2 x - 12 } { x - 6 }$

D) $\frac { ( x + 6 ) ^ { 2 } } { 2 }$

Question

Divide.
-$$\frac { x ^ { 2 } + 8 x + 12 } { x + 2 } \div \frac { x ^ { 2 } - 36 } { 2 x - 12 }$$
A) 2
B) $\frac { 1 } { 2 }$

C) $\frac { 2 x - 12 } { x - 6 }$

D) $\frac { ( x + 6 ) ^ { 2 } } { 2 }$

Quizplus · Accepted Answer

To solve this problem, we first simplify each fraction and then perform the division. 1. Simplify the numerator of the first fraction: $\frac { x ^ { 2 } + 8 x + 12 } { x + 2 }$. Factoring the numerator, we get $x^2 + 8x + 12 = (x + 6)(x + 2)$. So, the fraction simplifies to $x + 6$ after dividing by $x + 2$.2. Simplify the denominator of the second fraction: $\frac { x ^ { 2 } - 36 } { 2 x - 12 }$. Factoring the numerator, we get $x^2 - 36 = (x + 6)(x - 6)$, and the denominator can be factored as $2(x - 6)$. So, the fraction simplifies to $\frac {x + 6}{2}$.3. Perform the division: $\frac{x + 6}{1} \div \frac{x + 6}{2} = (x + 6) \times \frac{2}{x + 6} = 2$.Therefore, the correct answer is 2.

Divide - x2+8x+12x+2÷x2−362x−12\frac { x ^ { 2 } + 8 x + 12 } { x + 2 } \div \frac { x ^ { 2 } - 36 } { 2 x - 12 }x+2x2+8x+12​÷2x−12x2−36​

Divide
- $\frac { x ^ { 2 } + 8 x + 12 } { x + 2 } \div \frac { x ^ { 2 } - 36 } { 2 x - 12 }$