What is the tangent of 2/(x-1) ?

The tangent of 2/(x-1) is y=-2/((a_{0)-1)^2}x+(4a_{0}-2)/((a_{0)-1)^2}

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tangent of 2/(x-1)

tangent of

\frac{2}{x - 1}

y = - \frac{2}{( a _{0} - 1 ) ^{2}} x + \frac{4 a _{0} - 2}{( a _{0} - 1 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 1})

Find the slope of

y = \frac{2}{x - 1} : \frac{d y}{d x} = - \frac{2}{( x - 1 ) ^{2}}

Compute the slope of

y = \frac{2}{x - 1}

x = a_{0} : m = - \frac{2}{( a _{0} - 1 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 1 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 1}) : y = - \frac{2}{( a _{0} - 1 ) ^{2}} x + \frac{4 a _{0} - 2}{( a _{0} - 1 ) ^{2}}

y = - \frac{2}{( a _{0} - 1 ) ^{2}} x + \frac{4 a _{0} - 2}{( a _{0} - 1 ) ^{2}}

\int x^{- \frac{7}{3}} d x

\frac{d}{d x} (625 sin (5 x))

\int \frac{32 x ^{2}}{( x - 6 ) ( x + 2 ) ^{2}} d x

\int x^{3} x^{2} + 26 d x

\frac{1}{( s ( s ^{2} + 0.4 s + 4 ) )}

What is the tangent of 2/(x-1) ?
The tangent of 2/(x-1) is y=-2/((a_{0)-1)^2}x+(4a_{0}-2)/((a_{0)-1)^2}