Find the equation of the tangent line to the graph of

Question

f(x) =
2x − 6/x + 1
at the point at which
x = 0.
(Let x be the independent variable and y be the dependent variable.)

I got this question wrong. I thought the answer would be y=-4x-6
I followed the following steps:
1) Find the derivative
2) Plug 0 into the derivative to get the slope
3) Plug 0 into the original function to get y
4) find b
5) write equation with slope and b value

Answer 1

your method is ok, must be in the execution.
show your steps so I tell where you went wrong

Answer 2

For the derivative I got -4/(x+1)^2 by using the quotient rule. So then I plugged in zero and got -4 to be the slope.
Then when I plugged 0 into the original function and got 2(0)-6/1 which meant that y=-6. Then I tried to find b by doing 6=-4(0)+b and got b to be -6. Thus my answer was y=-4x-6 which unfortunately wasn't the answer.