What is the tangent of (x^2)/(x-7) ?

The tangent of (x^2)/(x-7) is y=(a_{0}^2-14a_{0})/((a_{0)-7)^2}x+(7a_{0}^2)/((a_{0)-7)^2}

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tangent of (x^2)/(x-7)

tangent of

\frac{x ^{2}}{x - 7}

y = \frac{a _{0}^{2} - 14 a _{0}}{( a _{0} - 7 ) ^{2}} x + \frac{7 a _{0}^{2}}{( a _{0} - 7 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}^{2}}{a _{0} - 7})

Find the slope of

y = \frac{x ^{2}}{x - 7} : \frac{d y}{d x} = \frac{x ^{2} - 14 x}{( x - 7 ) ^{2}}

Compute the slope of

y = \frac{x ^{2}}{x - 7}

x = a_{0} : m = \frac{a _{0}^{2} - 14 a _{0}}{( a _{0} - 7 ) ^{2}}

Find the line with slope m=

\frac{a _{0}^{2} - 14 a _{0}}{( a _{0} - 7 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}^{2}}{a _{0} - 7}) : y = \frac{a _{0}^{2} - 14 a _{0}}{( a _{0} - 7 ) ^{2}} x + \frac{7 a _{0}^{2}}{( a _{0} - 7 ) ^{2}}

y = \frac{a _{0}^{2} - 14 a _{0}}{( a _{0} - 7 ) ^{2}} x + \frac{7 a _{0}^{2}}{( a _{0} - 7 ) ^{2}}

\int \frac{1}{x - 3} d x

\int 5^{c o s (3 x)} sin (3 x) d x

f (x) = 9 e^{x}

e^{2 x} - x

10 y^{^{''}} - 10 y^{^{'}} + 125 y = 0

What is the tangent of (x^2)/(x-7) ?
The tangent of (x^2)/(x-7) is y=(a_{0}^2-14a_{0})/((a_{0)-7)^2}x+(7a_{0}^2)/((a_{0)-7)^2}