Simplify each expression.
$\frac{x^2-16}{16-x^2}$

• A. $-x^2$
• B. $-1$
• C. $x^2$
• D. $\frac{16}{x^2-16}$

Answer: (B)

Verified step by step guidance

1. Start by recognizing that both the numerator and denominator are differences of squares. Recall the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\).
2. Factor the numerator \(x^2 - 16\) as \((x - 4)(x + 4)\) using the difference of squares formula.
3. Factor the denominator \$16 - x^2\( as \)(4 - x)(4 + x)$, also using the difference of squares formula.
4. Notice that \((4 - x)\) can be rewritten as \(-(x - 4)\) because reversing the order changes the sign. Use this to rewrite the denominator as \(-(x - 4)(4 + x)\).
5. Now, write the fraction with the factored forms and simplify by canceling common factors. Pay attention to the negative sign factored out from the denominator.