What is the equation of the line tangent to # f(x)=(x-2)/(x^2-4) # at # x=-1 #? Calculus Derivatives Tangent Line to a Curve 1 Answer 1s2s2p May 25, 2018 #y=-x# Explanation: #f(x)=(x-2)/((x-2)(x+2))# (#a^2-b^2=(a+b)(a-b)#) #f(x)=1/(x+2)=(x+2)^-1# #f'(x)=-(x+2)^-2# #f'(-1)=-(-1+2)^-2=-(1)^-2=-1# #f(-1)=(-1+2)^-1=1^-1=1# #y-y_0=m(x-x_0)# #y-1=-1(x+1)# #y-1=-x-1# #y=-x# Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve #y=x^3-9x# at the point where #x=1#? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve #3y^2-2x^2=1#? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 1415 views around the world You can reuse this answer Creative Commons License