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

Step-by-step explanation:

The first step is obtain the derivative of the function y:

(Remember that the slope of the tangent line to any curve is given by its derivative).

Secondly, in order to obtain the equations of the tangent lines parallel to x - 2y = 5 we need to obtain the slope of this line, remember that the line equation is given by:

m : slope

b: y-intercept

Then, the slope of the line

is m = 1/2.

Then, the derivative of the function y must be 1/2:

When x = -3, y =(-3-1)/(-3+1)= 2, then one of the tangent lines must pass through the point (-3,2).

When x = 1, y = (1-1)(1+1)= 0, then the other tangent line must pass through the point (1, 0).

Finally, the point-slope equation of a line is given by:

Substituting our previous results we have the equations of the tangent lines:

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