# How do you find the equations of the tangent lines to the curve #y= (x-1)/(x+1)# that are parallel to the line x-2y=5?

We have two tangents which are

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To find the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y=5, we need to follow these steps:

- Differentiate the given curve equation y = (x-1)/(x+1) to find its derivative.
- Set the derivative equal to the slope of the given line x-2y=5, since parallel lines have the same slope.
- Solve the resulting equation for x to find the x-coordinate(s) of the point(s) where the tangent lines intersect the curve.
- Substitute the x-coordinate(s) into the original curve equation to find the corresponding y-coordinate(s).
- Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the curve and m is the slope, to write the equations of the tangent lines.

By following these steps, you will obtain the equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x-2y=5.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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