What is the Value of k in This SAT Math Problem?

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To solve for k in the equation (n/(n-1)) x (1/n) x (n/(n+1)) = 5/k, the left side simplifies to n/(n^2 - 1). This leads to the equation n/(n^2 - 1) = 5/k. Rearranging gives (n^2 - 1)/n = k/5. This indicates that k can be expressed as k = 5(n^2 - 1)/n for positive integers n and k. The discussion focuses on finding the correct value of k based on the derived formula.
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Homework Statement


(n/(n-1)) x (1/n) x (n/(n+1)) = 5/k for positive integers n and k, what is the value of k>




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The Attempt at a Solution



I multiplied the left side out to be (n/(n^2-1) and set it equal to 5/k

I got stuck right there.
 
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So what you've gotten is, n/(n2 - 1) = 5/k

If that's true, then we should have,

(n2 - 1)/n = k/5

Since we know that n != 0
 

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