what are the open intervals of increase for the given rational function below? f(x)=x - 2/x² - 2x. no…

Explanation:

Step1: Simplify the function

First, factor the denominator: $f(x)=\frac{x - 2}{x(x - 2)}=\frac{1}{x},x\neq0,2$.

Step2: Find the derivative

The derivative of $y = \frac{1}{x}=x^{-1}$ using the power - rule $(x^n)'=nx^{n - 1}$ is $y'=-x^{-2}=-\frac{1}{x^{2}}$.

Step3: Determine where the derivative is positive

Since $y'=-\frac{1}{x^{2}}<0$ for all $x\neq0$, the function has no intervals where it is increasing.

Answer:

No intervals of increase exist for this function.