I need help Simplifying this expression

Question

2j+6/ j² -6j-27

 

 i solved the whole thing and ended up with j= 9 (equal sign with a slash through it) but Ive learned there should be another value I'm very stuck on this and I need help

Answer 1

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.