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Problem 8 Medium Difficulty

5-8 Find an equation of the tangent line to the curve at the given point.
$y=\frac{2 x+1}{x+2}, \quad(1,1)$

Answer

$y=\frac{1}{3} x+\frac{2}{3}$

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Video Transcript

So we have. Why equals two X plus one pullers X plus two. We need to find attention line to this curve at the point one. What? Well, first, we're gonna use the question rule. Remember, that means numerator. Prime Time's the denominator. My house numerator times about on enterprise. Lower denominators cleared, so there's two times X plus two minus two x plus one times one allover experts too squared, which is two x plus four bias two X minus one longer X squared clothes for X clothes for which is the two x minus two X cancels out. That's just three over X squared plus four x plus four Know Mexico's one. He's what crime Go to squared close four times one plus four, which is pretty nights, which is 1/3 and remembers. That's the equation of the tangent line. That's why that's why is equal to, um, chose explain expects love. Where is as prime? That's not so. That's not why not. Here is 11 You just showed that and, well, third, so equations. My minus one is equal to 1/3 times X minus one. In other words, why 0 to 1 X minus one there plus one, which is 3/3 so that 1/3 thanks. Lions close 2/3

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