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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  • 1 decade ago
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    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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