Try to factor $9x^2 - 25$ using the difference of squares pattern $a^2 - b^2 = (a - b)(a + b)$, then rewrite the whole fraction using those factors.

After factoring, see if the numerator and denominator share a common factor. Use the condition $x \ne -\frac{5}{3}$ to decide what you are allowed to cancel.

In Desmos, type y = (9x^2 - 25)/(3x + 5) to graph the original rational expression.

Type each option as its own function, for example y = 3x - 5, y = 3x + 5, y = 9x - 25, and y = (3x - 5)/(3x + 5). You will now see multiple graphs on the same axes.

Look for the choice whose graph lies exactly on top of the graph of the original expression for all $x$ where the original function is defined (excluding the point where $3x + 5 = 0$). The expression whose graph matches the original everywhere in its domain is the equivalent expression.

Look at the numerator $9x^2 - 25$. Notice that $9x^2$ is a perfect square ($(3x)^2$) and $25$ is also a perfect square ($5^2$). An expression of the form $a^2 - b^2$ can be factored using the difference of squares formula:

Apply the formula with $a = 3x$ and $b = 5$.

So the whole expression becomes

In the fraction

there is a common factor of $3x + 5$ in the numerator and the denominator. Because the problem states $x \ne -\frac{5}{3}$, the denominator $3x + 5$ is not zero, so it is safe to cancel that factor:

This leaves the remaining numerator factor as the simplified expression.

After simplifying, the original expression is equal to $3x - 5$ (for $x \ne -\frac{5}{3}$). Among the answer choices, this corresponds to choice A: $3x - 5$.