Stephanie M. answered 06/10/15
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So, I'm guessing you did this:
(2j + 6) / (j2 - 6j - 27)
(2(j + 3)) / ((j - 9)(j + 3))
2 / (j - 9)
Then, you rightly decided that j - 9 ≠ 0, or j ≠ 9, since that would require us to divide by 0.
All you're missing is that, even though you cancelled the (j + 3) term out so it doesn't appear in the final version, it's still a problem for us if j + 3 = 0, or j = -3. That's because, in the original expression, if j = -3 you'll get:
(2(-3) + 6) / ((-3)2 - 6(-3) - 27)
(-6 + 6) / (9 + 18 - 27)
0 / 0
Even though the numerator is also 0, we're still dividing by 0, which gives you an undefined answer. So, you should also say that j ≠ -3.
Keep in mind that you're not solving this expression (since there's no equals sign), just simplifying it. So the values you're getting are restrictions on the domain (what j can't equal), not solutions.