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

$\frac{3x+5}{\left(x+2\right)\left(x+5\right)}$

$\frac{3x^2+15}{\left(x+2\right)\left(x+5\right)}$

$\frac{3x+15}{\left(x+2\right)\left(x+5\right)}$

$\frac{3x^2+5}{\left(x+2\right)\left(x+5\right)}$

Verified step by step guidance

Identify the original expression: $\frac{3}{x+2}$, which has the denominator $x+2$.

Note the desired denominator: $\left(x+2\right)\left(x+5\right)$, which is the original denominator multiplied by $x+5$.

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: $\frac{3 \cdot (x+5)}{(x+2) \cdot (x+5)}$.

Distribute the 3 in the numerator: $3 \cdot (x+5) = 3x + 15$.

Write the final equivalent expression as $\frac{3x + 15}{(x+2)(x+5)}$.

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