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Quotient rule question!

a curve is defined by the equation y = x + 2 / (x - 1)^2

a) find equation of the tangent to the curve at the point where x = 0
it is y = 5x + 2

b) find the coordinates of the point where the tangent crosses the curve again.
I tried to use simultaneous equation to solve it but I do not get anywhere with it. Can someone point me in the right direction?
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davros
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Original post by Zevo
a curve is defined by the equation y = x + 2 / (x - 1)^2

a) find equation of the tangent to the curve at the point where x = 0
it is y = 5x + 2

b) find the coordinates of the point where the tangent crosses the curve again.
I tried to use simultaneous equation to solve it but I do not get anywhere with it. Can someone point me in the right direction?


So assuming your part (a) is correct, you want to solve

5x + 2 = x + 2/(x-1)^2

Multiply both sides by (x-1)^2 and rearrange. This will give you a nasty looking cubic but remember you already know one point where the tangent meets the curve so you can factor this out.

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