Question

I also need help with (x)/(x+4)+(4)/(x+4)+2=0. My book says there is no solution, but I got one. I got -6 equals x (the x+4's cancel each other out so x+4 +2=0 is left. Then I subtracted the two, got x+4=-2. I subtracted the four and got x=-6).

Answer 1

no, you are doing some very "creative" math there


let's multiply each term by x+4, that will cancel out the x+4 in the first two terms

x + 4 + 2(x+4) = 0
3x = -12
x = -4

BUT, when we test this answer, we would be dividing by zero, which of course if a big NO-NO
So the answer we got, does not work, so there is no solution.
Your book is right.