SOLUTION: Please help me solve this equation: 6x/x+2-6= x-18/x-2
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Question 238261: Please help me solve this equation: 6x/x+2-6= x-18/x-2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'm reasonably certain you mean:
Although there is at least two other interpretations possible.
Be that as it may, you are going to get an answer to what I think it means.
None of the denominators have any factors in common, so the LCD is just the product of all the denominators:
(x\ -\ 2)\ =\ (x^2\ -\ 4))
Apply the common denominator:
}{x^2-4}\ -\ \frac{6(x^2-4)}{x^2-4}\ =\ \frac{(x-18)(x+2)}{x^2-4})
Multiply by the common denominator:
\ -\ 6(x^2\ -\ 4)\ =\ (x\ -\ 18)(x\ +\ 2))
Distribute to remove the parentheses and combine like terms. (verification of this next step is left as an exercise for the student)
Solve for 
. Hint: It factors. Remember to check both roots for validity and for inclusion in the domain of the original equation.
John
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