Divide.
-$$\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$$
A) $\frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 2 ) ^ { 2 } }$

B) $- \frac { x - 6 } { x - 1 }$

C) $\frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 2 ) ^ { 2 } ( x - 1 ) }$

D) $\frac { ( x - 1 ) ^ { 3 } } { ( x + 2 ) ^ { 2 } ( x - 6 ) }$

Question

Divide.
-$$\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$$
A) $\frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 2 ) ^ { 2 } }$

B) $- \frac { x - 6 } { x - 1 }$

C) $\frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 2 ) ^ { 2 } ( x - 1 ) }$

D) $\frac { ( x - 1 ) ^ { 3 } } { ( x + 2 ) ^ { 2 } ( x - 6 ) }$

Quizplus · Accepted Answer

To divide two fractions, we flip the second fraction and multiply by its reciprocal.

$$\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 } = \frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \cdot \frac { x ^ { 2 } - 8 x + 12 } { x ^ { 2 } - 2 x + 1 }$$

Now we can factor the numerator and denominator of each fraction.

$$\frac { (x-1)(x-2) } { (x+2)(x+2) } \cdot \frac { (x-6)(x-2) } { (x-1)(x-1) }$$

We can cancel out the common factors in the numerator and denominator.

$$\frac { (x-2)(x-6) } { (x+2)(x-1) }\cdot \frac { 1 } { (x-1) }$$

Simplifying further, we get:

$$\frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 2 ) ^ { 2 } ( x - 1 ) }$$

Therefore, the correct choice is (C).

Divide - x2−3x+2x2+4x+4÷x2−2x+1x2−8x+12\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }x2+4x+4x2−3x+2​÷x2−8x+12x2−2x+1​

Divide
- $\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$