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

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

Answer: (C)

Verified step by step guidance

1. Identify the original expression: \(\frac{3}{x+2}\), which has the denominator \(x+2\).
2. Note the desired denominator: \(\left(x+2\right)\left(x+5\right)\), which is the original denominator multiplied by \(x+5\).
3. To rewrite the expression with the new denominator, multiply both the numerator and denominator of the original fraction by \(x+5\) to keep the value equivalent. This gives: \(\frac{3 \cdot (x+5)}{(x+2) \cdot (x+5)}\).
4. Distribute the 3 in the numerator: \$3 \cdot (x+5) = 3x + 15$.
5. Write the final equivalent expression as \(\frac{3x + 15}{(x+2)(x+5)}\).