What is the simplified form of 5/(x/y + 3)?

To simplify the expression ( \frac{5}{\left(\frac{x}{y}\right) + 3} ), we need to combine the terms in the denominator into a single fraction.

Starting with ( \frac{x}{y} + 3 ), we can rewrite 3 as ( \frac{3y}{y} ) in order to have a common denominator. This gives us:

[

\frac{x}{y} + 3 = \frac{x}{y} + \frac{3y}{y} = \frac{x + 3y}{y}

]

Now, substituting this back into the original expression, we have:

[

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

]

When dividing by a fraction, it is equivalent to multiplying by its reciprocal. So we can rewrite the expression as:

[

5 \times \frac{y}{x + 3y} = \frac{5y}{x + 3y}

]

This reveals that the simplified form of ( \frac{5}{\left(\frac{x}{y}\right) + 3} ) is indeed ( \frac{