What is the equation of the line tangent to # f(x)=(x-2)/(x^2-4) # at # x=-1 #?

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Answer 1 · 2018-05-25T10:50:59

#y=-x#

#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#