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How do I simplify this? This is the LHS of the equation and I need it to equal the RHS, which is $2-1/k+!$

$$2−\frac{k^2+k+1}{k(k+1)2}$$

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You should reduce to same denominator. –  zozoens Jan 30 at 13:16
    
how do I go about this since k^2+k+1 is not factorable? –  Lil Jan 30 at 13:17
    
Just say that $2 = \frac{2k(k+1)}{k(k+1)}$, and simplify what you get in the numerator (where you should be able to factor out $k$). –  zozoens Jan 30 at 13:18
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Could you improve the formatting? The denominator of the LHS looks odd, and I have no idea what the RHS is what does "+!" mean? –  MPW Jan 30 at 13:27
    
math.stackexchange.com/questions/656791/… the second to last line in the first users answer. I don't understand how they went from the second to last line to the solution –  Lil Jan 30 at 13:29

1 Answer 1

What was written in the question you reference is $$2-\{\frac{k^2+k+1}{k(k+1)^2}\} \leq 2-\frac{k(k+1)}{k(k+1)^2}$$ Note that it is not an equality. The numerator on the right expands to $k^2+k$, so the quantity being subtracted on the left is larger than the quantity being subtracted on the left. This justifies the $\le$ sign, which could have been $\lt$

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