# 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 = 2#?

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#### Explanation

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Have a look:

which gives yu two equations:

and

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#### Explanation

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Find the equations of the tangent lines to the curve

There is a bit of algebra and arithmetic for this. Let's focus on the reasoning and the calculus.

**One**

A line parallel to

**Two**

How do we find the slope of the tangent line? -- The derivative. So, we want the derivative to be

What is the derivative of

Use the quotient rule:

**Three**

Find

So

and

**Four**

Find the

**Five**

Find the equations of the lines:

through

and through

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