Subtract the following rational expressions and write the difference in simplest form if possible.
$\frac{3}{x}-\frac{2}{x+2}$

• A. $\frac{3x+6}{x^2+2x}$
• B. $\frac{x+6}{x+2}$
• C. $\frac{x+6}{x^2+2x}$
• D. $\frac{3}{x^2+2x}$

Answer: (C)

Verified step by step guidance

1. Identify the two rational expressions to subtract: \(\frac{3}{x} - \frac{2}{x+2}\).
2. Find the least common denominator (LCD) of the two fractions. Since the denominators are \(x\) and \(x+2\), the LCD is their product: \(x(x+2)\).
3. Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: \(\frac{3}{x} = \frac{3(x+2)}{x(x+2)}\) and \(\frac{2}{x+2} = \frac{2x}{x(x+2)}\).
4. Subtract the numerators over the common denominator: \(\frac{3(x+2) - 2x}{x(x+2)}\).
5. Simplify the numerator by distributing and combining like terms: \$3x + 6 - 2x = x + 6\(, so the expression becomes \)\frac{x + 6}{x^2 + 2x}$.