In: Math

# Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.

Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.

## Solutions

##### Expert Solution

Given: $$y=\frac{x-1}{x+1}$$

$$\frac{d y}{d x}=\frac{x+1-(x-1)}{(x+1)^{2}}=\frac{2}{(x+1)^{2}}$$

So, $$\frac{2}{(x+1)^{2}}=\frac{1}{2}$$

or $$x^{2}+2 x-3=0$$

$$(x-1)(x+3)=0$$

$$x=1,-3$$

For $$x=1, y=0$$

For $$x=-3, y=2$$

So, equation of tan gents:

$$(y-0)=\frac{1}{2}(x-1)$$

$$\& \quad(y-2)=\frac{1}{2}(x+3)$$

$$x-2 y-1=0$$

$$\& \quad x-2 y+7=0$$