After you factor out $(x+5)$ from the numerator, check whether the remaining factor can be simplified further by factoring out a constant.

Factor $x^2 + 6x + 5$ into two binomials. Then see if any factor in the numerator also appears in the denominator so that the fraction can be simplified.

When you cancel a factor, make sure that factor is never zero for the allowed values of $x$ (here, $x \ne -5$ and $x \ne -1$).

Type the original expression as a function, for example f(x) = ((3x+2)(x+5) - 5(x+5))/(x^2+6x+5) and press Enter. Be aware that the graph will have holes or undefined points at $x=-5$ and $x=-1$.

Define each choice as its own function, for example g(x) = 3(x-1)/(x+1), h(x) = 3(x+1)/(x-1), etc. (one for each option), making sure to type them exactly as written.

Either (a) look at the graphs and see which choice’s graph lies exactly on top of the graph of $f(x)$ (except at the excluded $x$-values), or (b) use a table for each function and compare values of $f(x)$ with each option at several $x$-values (not equal to $-5$ or $-1$). The option whose values always match $f(x)$ is the equivalent expression.

Look at the numerator:

Both terms contain $(x+5)$, so factor $(x+5)$ out:

Now simplify inside the brackets:

so the numerator becomes $(x+5)(3x - 3)$.

Now factor $3$ out of $3x - 3$:

So the entire numerator is

Factor the quadratic in the denominator:

We need two numbers that multiply to $5$ and add to $6$. Those numbers are $1$ and $5$, so

Now the whole fraction is

Since $x \ne -5$, the factor $(x+5)$ is never $0$, so we can safely cancel $(x+5)$ from numerator and denominator:

This simplified expression matches answer choice A, so the correct answer is $\dfrac{3(x-1)}{x+1}$.