# What is the equation of the tangent line of #f(x) = (e^(x)-1)/(x^2-1)# at #x=2#?

##### 1 Answer

Equation of tangent is

#### Explanation:

The slope of the tangent is the same as the slope of curve at that point, which is given by the value of derivative of the function at that point.

Hence, slope of tangent to curve

Now

and using quotient rule

=

and slope at

Hence, equation of tangent is

or

or

graph{(9y+(e^2-4)x-5e^2+11)(x^2y-y-e^x+1)=0 [-4.785, 5.215, -1.18, 3.82]}