What is the tangent of 2/(x-3) ?

The tangent of 2/(x-3) is y=-2/((a_{0)-3)^2}x+(4a_{0}-6)/((a_{0)-3)^2}

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tangent of 2/(x-3)

tangent of

\frac{2}{x - 3}

y = - \frac{2}{( a _{0} - 3 ) ^{2}} x + \frac{4 a _{0} - 6}{( a _{0} - 3 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 3})

Find the slope of

y = \frac{2}{x - 3} : \frac{d y}{d x} = - \frac{2}{( x - 3 ) ^{2}}

Compute the slope of

y = \frac{2}{x - 3}

x = a_{0} : m = - \frac{2}{( a _{0} - 3 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 3 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 3}) : y = - \frac{2}{( a _{0} - 3 ) ^{2}} x + \frac{4 a _{0} - 6}{( a _{0} - 3 ) ^{2}}

y = - \frac{2}{( a _{0} - 3 ) ^{2}} x + \frac{4 a _{0} - 6}{( a _{0} - 3 ) ^{2}}

\int \frac{1}{x ^{2} - 8 x + 65} d x

2 x + 1

\int 5^{- 5 x} d x

(x^{9} - 3 x)^{- 2}

\int (y + 1) d y

What is the tangent of 2/(x-3) ?
The tangent of 2/(x-3) is y=-2/((a_{0)-3)^2}x+(4a_{0}-6)/((a_{0)-3)^2}