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: $(x+2)(x+5)$, which is the original denominator multiplied by the new factor $(x+5)$.

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.

Write the new expression as $\frac{3 \cdot (x+5)}{(x+2)(x+5)}$.

Expand the numerator by distributing 3: \$3 \cdot (x+5) = 3x + 15$, so the equivalent expression is $\frac{3x + 15}{(x+2)(x+5)}$.

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