You’re welcome

]]>Thank you.

]]>Check out this helpful post from Chris McMullen’s blog titled Expanded Distribution Has Expanded ]]>

Are you talking about the “Check” in Example 4? There is a lot packed into that little space, so I can see how that might need a little more explanation.

After finding that x = –5/2 +/– sqrt(17)/2, I plugged this into the equation x^2 + 5x + 6 = 4 to check that the left-hand side equals 4. When I plugged this in, I got six terms. Three terms come from applying the “foil” method to square –5/2 +/– sqrt(17)/2, two terms come from multiplying 5 by x, and the last term is 6. The two terms with the sqrt(17) cancel out. For the remaining terms, make a common denominator and you should get 25/4 + 17/4 – 50/4 + 24/4 = 16/4 = 4, which shows that this solution works.

It’s easier to check the answer using a calculator with decimals. On a calculator, the two answers work out to –0.4384 and –4.5616 (to 4 decimal places), and when x^2 + 5x + 6 = 4 is evaluated for each answer, you should get approximately 4 (apart from slight round-off error). Better yet, plug the answers into the original equation 1/(x+2) = (3+x)/4 to check that they satisfy the original equation.

I hope this helps.

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