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).
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.
To solve the equation (x)/(x+4) + (4)/(x+4) + 2 = 0, let's go through the steps:
Step 1: Combine like terms
(x)/(x+4) + (4)/(x+4) + 2 = 0
Step 2: Find a common denominator
Both fractions have the same denominator (x+4), so no further steps are needed.
Step 3: Combine the fractions
(x + 4 + 4)/(x + 4) + 2 = 0
(x + 8)/(x + 4) + 2 = 0
Step 4: Combine the fractions and eliminate the denominator
(x + 8 + 2(x + 4))/(x + 4) = 0
(x + 8 + 2x + 8)/(x + 4) = 0
(3x + 16)/(x + 4) = 0
Step 5: Multiply both sides by the common denominator (x + 4)
3x + 16 = 0
Step 6: Solve for x
3x = -16
x = -16/3
By following these steps, we find that x = -16/3. However, let's verify the validity of our solution.
If we substitute x = -16/3 back into the original equation, we get:
(-16/3) / (-16/3 + 4) + (4) / (-16/3 + 4) + 2 = 0
After simplifying, we get:
(-16/3) / (4/3) + (4) / (4/3) + 2 = 0
(-16/3) * (3/4) + 12/3 + 2 = 0
-4 + 4 + 2 = 0
2 ≠ 0
As we can see, when we substitute x = -16/3, the equation does not hold true. Therefore, the solution x = -16/3 is not valid.
Thus, there is no solution to the equation (x)/(x+4) + (4)/(x+4) + 2 = 0.