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# find the equation of the tangent line to the curve at the given point.

y = x - 1 / x - 2 at (3,2).

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- Mrs. AkaLv 51 decade agoFavorite Answer
y = (x - 1)/(x - 2)

Take the derivative using the Quotient rule:

y' = (x - 2)(1) - (x - 1)(1)/(x - 2)^2

Clean up:

y' = (x - 2) - (x - 1)/(x - 2)^2

y' = (x - 2) + (-x + 1)/(x - 2)^2

y' = (-1)/(x - 2)^2

The "(-1)/(x - 2)^2" part gives the formula for slope...plug in 3 for x (since x in (3, 2) is 3):

m = (-1)/(3 - 2)^2

m = (-1)/(1)^2

m = (-1)/(1)

m = -1

Write the equation using m = -1 and the point (3, 2):

y - 2 = -1(x - 3)

y - 2 = -1x + 3

y = -1x + 5

This is the equation of the tangent line.

Hope that helps!

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