Divide.
-$$\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }$$
A) $\frac { x - 3 } { 5 x - 2 }$

B) $- \frac { ( x + 3 ) ( x - 3 ) ^ { 2 } } { ( 5 x + 2 ) ( 5 x - 2 ) ^ { 2 } }$

C) $- \frac { x + 3 } { 5 x + 2 }$

D) $\frac { x + 3 } { 5 x + 2 }$

Question

Divide.
-$$\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }$$
A) $\frac { x - 3 } { 5 x - 2 }$

B) $- \frac { ( x + 3 ) ( x - 3 ) ^ { 2 } } { ( 5 x + 2 ) ( 5 x - 2 ) ^ { 2 } }$

C) $- \frac { x + 3 } { 5 x + 2 }$

D) $\frac { x + 3 } { 5 x + 2 }$

Quizplus · Accepted Answer

To divide two fractions, we multiply the first fraction with the reciprocal of the second fraction. In this case, we have
$$\frac{x^2-9}{25x^2-4} \cdot \frac{2-5x}{x-3}.$$
Now we factor the numerator and denominator of the first fraction:
$$\frac{(x+3)(x-3)}{(5x+2)(5x-2)} \cdot \frac{2-5x}{x-3}.$$
We can now cancel out the common factor of $(x-3)$ in the numerator and denominator:
$$\frac{(x+3)}{(5x+2)(5x-2)} \cdot \frac{-5(x-2)}{(x-3)}.$$
Simplifying this expression, we get
$$-\frac{(x+3)}{(5x+2)},$$
which is option (C).

Divide - x2−925x2−4÷x−32−5x\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }25x2−4x2−9​÷2−5xx−3​

Divide
- $\frac { x ^ { 2 } - 9 } { 25 x ^ { 2 } - 4 } \div \frac { x - 3 } { 2 - 5 x }$