Once you factor $x^2 - 16$, think about what the least common denominator of all three fractions should be so you can combine them into a single fraction.

After rewriting each fraction with the common denominator, put them over one denominator and simplify the entire numerator carefully by distributing and combining like terms.

When you have a single fraction, check if the numerator and denominator share a common factor that can be factored out and canceled (keeping in mind any values of $x$ that would make denominators zero).

Type f(x) = 4x/(x^2-16) + 3/(x+4) - 2/(x-4) into Desmos to graph the original expression.

Add four more functions: g1(x) = 5/(x-4), g2(x) = (x-4)/(x+4), g3(x) = 5x/(x^2-16), and g4(x) = 5/(x+4).

Zoom out and compare the graph of $f(x)$ with each $g_i(x)$. Ignore the vertical asymptotes (where denominators are zero) and focus on where the graphs overlap. The answer choice whose graph exactly coincides with $f(x)$ for all other $x$-values is the equivalent expression.

First, factor the denominator in the first fraction:

So the expression becomes

The least common denominator (LCD) of all three fractions is $(x-4)(x+4)$.

Rewrite each term so it has denominator $(x-4)(x+4)$:

• First term already has the LCD:

• Second term: multiply top and bottom by $(x-4)$:

• Third term: multiply top and bottom by $(x+4)$:

so the whole expression is

Now that all denominators are the same, combine the numerators over the common denominator $(x-4)(x+4)$:

Simplify the numerator:

• Distribute:

• Combine like terms:

So the expression simplifies to

Factor the numerator $5x - 20$:

So the expression is

For $x \ne 4$, the factor $(x-4)$ cancels from numerator and denominator, giving

which matches answer choice D.