Simplify each expression.
$\frac{x-7}{7-x}$

• A. $-x$
• B. $-1$
• C. $x$
• D. $\frac{7}{x-7}$

Answer: (B)

Verified step by step guidance

1. Look at the expression \(\frac{x-7}{7-x}\). Notice that the numerator and denominator look similar but in reverse order.
2. Recall that \(a - b = -(b - a)\), which means \(x - 7 = -(7 - x)\). This is a key property to simplify the fraction.
3. Rewrite the numerator using this property: \(x - 7 = -(7 - x)\), so the fraction becomes \(\frac{-(7 - x)}{7 - x}\).
4. Since the numerator is \(-(7 - x)\) and the denominator is \$7 - x\(, the fraction simplifies to \)-1\( because the \)(7 - x)$ terms cancel out.
5. Therefore, the simplified form of \(\frac{x-7}{7-x}\) is \(-1\).