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Numerade Educator

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Problem 54 Hard Difficulty

Find equations of the tangent lines to the curve

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

that are parallel to the line $ x - 2y = 2. $

Answer

$y=\frac{1}{2} x+\frac{7}{2}, \quad y=\frac{1}{2} x-\frac{1}{2}$

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Video Transcript

Hey, it's clear. So when you re here so you have X minus two. Why is equal to two and this continue Y is equal to 1/2 X minus one. This is the M, which is the slope of the line. So here we're gonna find the derivative of the curve. Why is equal to X alertness one over X plus one. The derivative is equal to one times next, plus one minus one term X minus one over X plus worn square which becomes equal to two over X plus one square. So this is the slope of the tension line to Wyatt X. So when we plug in, make this equal to one. Have we get when half is equal to two over X plus one square that's can be equal to negative three or one. So we're gonna get the Y coordinates. So when X is equal to negative three Well, why is equal to two when X is equal to one? Why is equal to zero? We're gonna pluck the points and slope into the point slope line equation. So for a negative three korma too, we get why is equal to 1/2 x minus and negative. Three less, too, which is equal to one. Have X less stubborn has for one comma zero we have. Why is equal to one, huh X minus one plus zero, which is equal to 1/2 X minus one her.