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1. The equation of line of tangent is :

   y=1/2x+7/2 and y=1/2x-1/2.

   According to the statement

   we have to find the equation of the line with the help of the given curve.

   So, For this purpose, we know that the

   The given information is:

   The equations of the tangent lines to the curve is y= (x-1)/(x+1) and the that are parallel to the line x-2y = 2.

   So,

   A line parallel to x-2y = 2 must have the same slope. The slope of this line is 1/2.

   So we want the slope of the tangent line to be 1/2.

   Now we find the derivative of the y= (x-1)/(x+1)

   So,

   By quotient rule the derivative become

   y’= (x(x+1)-(x-1)*1)/(x+1)^2

   y’ = 2/(x+1)^2

   So,

   Now find the value of the x with the help of y’.

   So,

   2/(x+1)^2 = 1/2

   And solve it then

   x = 1 and -3.

   So, x = 1 and x = -3.

   Now, the value of y become:

   At x = 1, y = 0 and

   x = -3, y = 2.

   then

   The equation of lines with point (1,0) and slope 1/2.

   And The equation of lines with point (-3,2) and slope 1/2.

   So, The equation of line of tangent is :

   y=1/2x+7/2 and y=1/2x-1/2.

   Learn more about equation of line here

   https://brainly.com/question/13763238

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   Question:

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

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