Calculus: I keep getting this question wrong can you help?

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y = -2x/(x²+1)
y' = [-2(x²+1) + 2x(2x)]/(x²+1)² = (4x²-2x²-2)/(x²+1)² = 2(x²-1)/(x²+1)²

y'(0) = -2
y'(1) = 0

The tangent line at the origin has slope -2 and passes through point (x,y) = (0,0):
y = -2x
The tangent line at the point (1,-1) has slope 0 (horizontal) and passes through the point (x,y) = (1,-1):
y = -1
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