Context: f(x)= x 2 −16 5x−20 ​ Explain

It seems like there's a formatting issue with your question. However, I'm assuming you're asking about the function f(x) = (x^2 - 16) / (5x - 20).

Here's a step-by-step explanation:

1. The function f(x) = (x^2 - 16) / (5x - 20) is a rational function, which is a ratio of two polynomials.

2. The numerator, x^2 - 16, is a quadratic polynomial. It can be factored using the difference of squares formula, a^2 - b^2 = (a - b)(a + b). So, x^2 - 16 = (x - 4)(x + 4).

3. The denominator, 5x - 20, is a linear polynomial. It can be factored by taking out the common factor, which is 5. So, 5x - 20 = 5(x - 4).

4. Substituting the factored forms back into the function, we get f(x) = [(x - 4)(x + 4)] / [5(x - 4)].

5. We can see that (x - 4) is a common factor in the numerator and the denominator. As long as x ≠ 4 (because division by zero is undefined), we can cancel out this common factor.

6. After canceling out the common factor, the function simplifies to f(x) = (x + 4) / 5.

7. So, the function f(x) = (x^2 - 16) / (5x - 20) simplifies to f(x) = (x + 4) / 5, for x ≠ 4.