# What is the equation of the tangent line of #f(x)=(x-2)/(x-3)+lnx/(3x)-x# at #x=2#?

To find the equation of the tangent line of the function we can start by taking its derivative, which will give us the slope of the tangent line to the curve.

I prefer to rewrite using products rather than quotients to avoid the quotient rule, but either approach will work.

You could choose to simplify, but since we're given a value I will save time by plugging it in now and evaluating.

We can put these values into the generic equation above.

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The equation of the tangent line of f(x) at x=2 is y = -1.

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