What is the tangent of (5x)/(x-2) ?

The tangent of (5x)/(x-2) is y=-(10)/((a_{0)-2)^2}x+(5a_{0}^2)/((a_{0)-2)^2}

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tangent of (5x)/(x-2)

tangent of

\frac{5 x}{x - 2}

y = - \frac{10}{( a _{0} - 2 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} - 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{5 a _{0}}{a _{0} - 2})

Find the slope of

y = \frac{5 x}{x - 2} : \frac{d y}{d x} = - \frac{10}{( x - 2 ) ^{2}}

Compute the slope of

y = \frac{5 x}{x - 2}

x = a_{0} : m = - \frac{10}{( a _{0} - 2 ) ^{2}}

Find the line with slope m=

- \frac{10}{( a _{0} - 2 ) ^{2}}

and passing through

(a_{0}, \frac{5 a _{0}}{a _{0} - 2}) : y = - \frac{10}{( a _{0} - 2 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} - 2 ) ^{2}}

y = - \frac{10}{( a _{0} - 2 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} - 2 ) ^{2}}

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 2 x} d x

\int_{0}^{\infty} e^{- u} d u

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

t \to 0 lim (\frac{( 3 e ^{t} - 3 )}{t})

\frac{d}{d x} (- \frac{2 x}{( x ^{2} + 3 ) ^{2}})

What is the tangent of (5x)/(x-2) ?
The tangent of (5x)/(x-2) is y=-(10)/((a_{0)-2)^2}x+(5a_{0}^2)/((a_{0)-2)^2}