equation of tangent line y=(2x)/x+1 (1,1)?

Answer 1

f (x) = 2x / (x + 1)
f ` (x) = [ 2 (x + 1) - (2x) ] / (x + 1)²
f `(1) = 2 / 4 = 1 / 2
m = 1 / 2
tangent passes thro` (1 , 1)
y - 1 = (1/2) (x - 1)
y = (1/2) x + 1/2 is equation of tangent line.

Answer 2

y=(2x)/(x+1) (1,1)
y' =[2(x+1)-2x]/(x+1)^2
y' = 1/(x+1)^2
y'(1) = 1/4
y = x/4 +b
1 = 1/4 +b
b = 3/4
y = x/4 + 3/4 <-- Equatin of tangent