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

A) $\frac{x-3}{2 x-5}$

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

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

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

Question

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

A) $\frac{x-3}{2 x-5}$

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

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

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

Quizplus · Accepted Answer

To solve the expression, first rewrite the division as multiplication by the reciprocal: $\frac{x^{2}-9}{4 x^{2}-25} \times \frac{5-2x}{x-3}$. Factor the numerators and denominators: $\frac{(x-3)(x+3)}{(2x-5)(2x+5)} \times \frac{-(2x-5)}{x-3}$. Cancel out common terms: $-(x+3)/(2x+5)$.