Rewrite the expression $\frac{3}{x+2}$ into an equivalent expression having a denominator of $(x+2)(x+5)$.

• A. $\frac{3x+5}{(x+2)(x+5)}$
• B. $\frac{3x^2+15}{(x+2)(x+5)}$
• C. $\frac{3x+15}{(x+2)(x+5)}$
• D. $\frac{3x^2+5}{(x+2)(x+5)}$

Answer: (C)

Verified step by step guidance

1. Start with the original expression: \(\frac{3}{x+2}\).
2. To rewrite this fraction with the denominator \(\left(x+2\right)\left(x+5\right)\), multiply both the numerator and the denominator by the missing factor \(\left(x+5\right)\) to keep the value equivalent.
3. Set up the multiplication: \(\frac{3}{x+2} \times \frac{x+5}{x+5} = \frac{3(x+5)}{(x+2)(x+5)}\).
4. Distribute the 3 in the numerator: \$3(x+5) = 3x + 15$.
5. Write the final equivalent expression as \(\frac{3x + 15}{(x+2)(x+5)}\).