What is the tangent of y= x/(x-5),(-1,a) ?

The tangent of y= x/(x-5),(-1,a) is

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tangent of y= x/(x-5),(-1,a)

tangent of

y = \frac{x}{x - 5}, (- 1, a)

y = - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )} x + a - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )} or y = - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )} x + a - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )}

Solution steps

Slope of the tangent line at

(- 1, a) : m = \frac{x - a ( x - 5 )}{( x - 5 ) ( x + 1 )}

Find the slope of

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

Solve

- \frac{5}{( x - 5 ) ^{2}} = \frac{x - a ( x - 5 )}{( x - 5 ) ( x + 1 )} : x = \frac{- 10 a + 120 a - 20}{2 ( - a + 1 )}, x = \frac{- 10 a - 120 a - 20}{2 ( - a + 1 )}; a \neq = 1

Find the tangent line at

x = \frac{- 10 a + 120 a - 20}{2 ( - a + 1 )} : y = - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )} x + a - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )}

Find the tangent line at

x = \frac{- 10 a - 120 a - 20}{2 ( - a + 1 )} : y = - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )} x + a - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )}

y = - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )} x + a - \frac{- 6 a ^{2} + 7 a - 5 a 6 a - 1 + 5 6 a - 1 - 1}{3 ( 120 a - 20 + 2 - 12 a )} or y = - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )} x + a - \frac{- 6 a ^{2} + 5 a 6 a - 1 + 7 a - 5 6 a - 1 - 1}{3 ( 2 - 12 a - 120 a - 20 )}

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