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Find an equation of the tangent line to the given curve at the specified point.

$ y = \frac {x^2 - 1}{x^2 + x + 1}, (1,0) $

$y=\frac{2}{3} x-\frac{2}{3}$

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Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Hey, it's from someone. You rain here, so we have. Why is equal to X square minus one all over X square plus X plus one. We're gonna use the quotient role to find the derivative when we get X square minus one The derivative X square plus X plus one minus X square minus one and the derivative of X square plus X plus one This is all over X square plus X plus one square. When we simplify this, we get X square. It was for X plus one while over at square, less X plus one square. So to find a slope of the tangent line at one comma zero we're gonna plug in X is equal to one into our derivative when we get 2/3. So we're gonna create a line Why is equal to 2/3 X minus one plus zero? This becomes equal to two birds. X minus 2/3