I need to see the steps for solving the following equation: Find the equation of the tangent line to the curve at the given points for y=x^2-1/x^2+x+1 (1,0). I know the answer is 2/3x-2/3 but I'm just not getting that when I try to derive the equation and then plug that answer into the line formula.

Find the equation of the tangent line to

f(x)=(x^2-1)/(x^2+x+1) at the point (1,0).

m = f’(1)

Use Quotient Rule:

f’(x) = ((x^2-1)’(x^2+x+1)–(x^2-1)(x^2+x+1)’)

/((x^2+x+1)^2)

f’(x) = (2x(x^2+x+1)–(x^2-1)(2x+1))

/((x^2+x+1)^2)

m = f’(1) = (2(3)–0)/(3^2) = 6/9 = 2/3

Tangent Line:

y–0 = 2/3 (x–1)

y = 2/3 x - 2/3

f(x)=(x^2-1)/(x^2+x+1) at the point (1,0).

m = f’(1)

Use Quotient Rule:

f’(x) = ((x^2-1)’(x^2+x+1)–(x^2-1)(x^2+x+1)’)

/((x^2+x+1)^2)

f’(x) = (2x(x^2+x+1)–(x^2-1)(2x+1))

/((x^2+x+1)^2)

m = f’(1) = (2(3)–0)/(3^2) = 6/9 = 2/3

Tangent Line:

y–0 = 2/3 (x–1)

y = 2/3 x - 2/3

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