# Consider the following function and point. f(x) = \frac{x + 2}{x - 2}, (3, 5) Find an equation...

## Question:

Consider the following function and point.

{eq}\displaystyle f(x) = \frac{x + 2}{x - 2}, (3, 5) {/eq}

Find an equation of the tangent line to the graph of f at the given point. Please show work.

## Tangent Line to a function

For a given differentiable function {eq}f(x) {/eq}, the tangent line with the function at a given point {eq}P(x_1,y_1) {/eq} is computed by:

{eq}y - y_1 = m(x - x_1) {/eq}

Where {eq}m {/eq} is the slope given by the first derivative of the function evaluated at {eq}x = x_1 {/eq}, that is {eq}m = f'(x_1) {/eq}.

## Answer and Explanation:

Let's begin by getting the derivative of the function.

{eq}\displaystyle f(x) = \frac{x + 2}{x - 2} \\ \displaystyle f'(x) = \frac{(x-2)(x+2)' -...

See full answer below.

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