SOLUTION: Find the gradient of the curve y = x + 4/(x-5) at the points where the curve crosses the x-axis

Question 1190872: Find the gradient of the curve y = x + 4/(x-5) at the points where the curve crosses the x-axis
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the gradient of the curve y = x + 4/(x-5) at the points where the curve crosses the x-axis
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Or ?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
y=0, then x=-4/(x-5)
x^2-5x=-4 multiplying through
x^2-5x+4=0
(x-4)(x-1)=0
x=4 and 1, so looking at (1, 0) and (4, 0)
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take the derivative:
y'=1-4/(x-5)^2
=1-[4/(x-5)^2]. When x=1 y'=1-(1/4) so slope is (3/4);when x=4 y'=-3

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