equation of the tangent line?

Question

(3x)/(x+1)
at point (1, 1.5)
i got
y=(3/4)x+(5/4)

Answer 1

f(x)=3x/(x+1)
--> f '(x)=(3x+3-3x)/(x+1)^2=3/(x+1)^2
tangent line:
y-yo=f '(xo)(x-xo)
<-->y=f '(1)(x-1)+1.5=3x/4-3/4+6/4=3x/4+3/4

y=3x/4+3/4

Answer 2

Also, be sure to check your work when you do problems like this. You'll note right off the bat that the point (1, 1.5) does not lie on the line y=(3/4)x + 5/4, so it obviously cannot be your tangent line.

Answer 3

y´= 1/(x+1)^2 *( 3x+3-3x) = 3/(x+1)^2
At(x=1 y´= 3/4 and and y=3/2
so y-3/2 = 3/4(x-1) so y= 3/4 x +3/4