Solve the following function with the independent variables given below

Question

Given: $f(x) = \frac{4}{\sqrt{x-4}}$

Solve: $\frac{f(x) - f(20)}{x-20}$

My solution: $\frac{(4x-80)\sqrt{x-4} - (x-4)(x-20)}{x-4}$

However, it says I am incorrect. Please Help. Thanks.

Answer 1

It's differentiation of $f(x)$ because $\frac{df}{dx}=\frac{f(a)-f(b)}{a-b}$.
We have $f(x)=\frac{4}{\sqrt{x-4}}$ $$\frac{df}{dx}=-\frac{2}{(x-4)\sqrt{(x-4)}}$$ put $x=20$ and get the answer.

Answer 2

$$\frac{f(x) - f(20)}{x-20}=\frac{\frac{4}{\sqrt{x-4}} - \frac{4}{\sqrt{20-4}}}{x-20}=\frac{\frac{4}{\sqrt{x-4}} - 1}{x-20}=\frac{\frac{4-\sqrt{x-4}}{\sqrt{x-4}}}{x-20}=\frac{4-\sqrt{x-4}}{(x-20)\sqrt{x-4}}$$