SOLUTION: can someone please help solve this problem Consider the solution of 8/(x+6) + 1/(3x+18) - 14/(4x+24) = 0 What is your LCM? (factors in parentheses, any order): Excluded so

Algebra ->  Rational-functions -> SOLUTION: can someone please help solve this problem Consider the solution of 8/(x+6) + 1/(3x+18) - 14/(4x+24) = 0 What is your LCM? (factors in parentheses, any order): Excluded so      Log On


   

Question 771303: can someone please help solve this problem
Consider the solution of 8/(x+6) + 1/(3x+18) - 14/(4x+24) = 0
What is your LCM? (factors in parentheses, any order):
Excluded solutions (lesser to greater, commas between):
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
This same question has just been asked four times under different categories.
The three summed expression use these completely factored denominators:
(1)_______ %28x%2B6%29
(2)_______ 3%2A%28x%2B6%29
(3)_______ 4%2A%28x%2B6%29

You want the simplest or "least" common multiple for all of those three expressions. The x+6 occurs ONE time at most in any of the expression.
The 3 occurs at most ONE time in any of the expressions.
The 4 occurs at most ONE time in any of the expressions.
The lowest common multiple, is then highlight%283%2A4%2A%28x%2B6%29%29 or in fully multiplied form, highlight%2812x%2B72%29


SOLVING THE EQUATION

Multiply both sides by 12x+72.

12%2A8%2B12-12%2A14=0
12%2A8-12%2A14%2B12=0
12%288-14%2B1%29=0
12%2A%28-5%29=0
highlight%28-60=0%29 FALSE STATEMENT!
The given equation has no solution.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
8%2F%28x%2B6%29+%2B+1%2F%283x%2B18%29+-+14%2F%284x%2B24%29+=+0

8%2F%28x%2B6%29+%2B+1%2F%283%28x%2B6%29%29+-+14%2F%284%28x%2B6%29%29 = 0

8%2F%28x%2B6%29+%2B+1%2F%283%28x%2B6%29%29+-+7%2F%282%28x%2B6%29%29 = 0

LCM = 6(x+6)