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I am currently stuck on an induction proof where I don't seem to understand why the positive 2(k + 1) becomes negative after giving both parts of the equation equal denominators. What is the reason for this? thank's a lot in advance!

If it is unclear what part of the equation I'm talking about, it is the 4th and 5th line.

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TheOnlyTater
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For convenience let us adapt some shorter forms. Let $a = 2k+1$, $b=k+2$, c = $k+1$ and $x = k(k+1)(k+2)$. Now observe the forth equation $$\frac{3}{2}-\frac{ab}{x} + \frac{c}{x}.$$ Now let us take $-1$ out as common factor, then $$\frac{3}{2}-1\left(\frac{ab}{x} - \frac{c}{x}\right).$$ We then have $$\frac{3}{2}-1\left(\frac{ab -c}{x}\right).$$

I hope this helps.

liamsi Meean
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