Divide.
-$$\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \div \frac { 4 x - 20 } { x ^ { 2 } + 12 x + 27 }$$
A) $\frac { ( x + 5 ) ( x + 3 ) } { x + 9 }$

B) $\frac { ( x + 5 ) ( x + 3 ) } { 4 ( x + 9 ) }$

C) $\frac { ( x - 5 ) ( x - 3 ) } { 4 ( x - 9 ) }$

D) $\frac { x + 9 } { ( x + 5 ) ( x + 3 ) }$

Question

Divide.
-$$\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \div \frac { 4 x - 20 } { x ^ { 2 } + 12 x + 27 }$$
A) $\frac { ( x + 5 ) ( x + 3 ) } { x + 9 }$

B) $\frac { ( x + 5 ) ( x + 3 ) } { 4 ( x + 9 ) }$

C) $\frac { ( x - 5 ) ( x - 3 ) } { 4 ( x - 9 ) }$

D) $\frac { x + 9 } { ( x + 5 ) ( x + 3 ) }$

Quizplus · Accepted Answer

When dividing fractions, we multiply by the reciprocal of the divisor fraction. So, we have:

$$\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \cdot \frac { x ^ { 2 } + 12 x + 27 } { 4 x - 20 }$$

Now, we can factor the expressions in the numerators and denominators:

$$\frac { ( x + 5 ) ( x - 5 ) } { ( x + 9 ) ^ { 2 } } \cdot \frac { ( x + 3 ) ( x + 9 ) } { 4 ( x - 5 ) }$$

We can simplify this expression by canceling out the common factors in the numerator and denominator:

$$\frac { ( x + 5 ) ( x + 3 ) } { 4 ( x + 9 ) }$$

Therefore, the correct answer is B.

Divide - x2−25x2+18x+81÷4x−20x2+12x+27\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \div \frac { 4 x - 20 } { x ^ { 2 } + 12 x + 27 }x2+18x+81x2−25​÷x2+12x+274x−20​

Divide
- $\frac { x ^ { 2 } - 25 } { x ^ { 2 } + 18 x + 81 } \div \frac { 4 x - 20 } { x ^ { 2 } + 12 x + 27 }$