SOLUTION: Solve the equation. 3/x+3/x-5=3x-12/x-5

Question 110624: Solve the equation.
3/x+3/x-5=3x-12/x-5
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

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Step 1 is to look at the domain of the function. Note that either x = 0 or x = 5 results in a 0 denominator, so the domain is all real except 0 and 5.
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Step 2 is to find the common denominator. The only factors we have are and , so the only common denominator is .
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Now we need to simplify and collect like terms.
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, after multiplication by

, after collecting terms and multiplying by -1
, after dividing by 3
, after factoring (given the difficulty level of this problem, I'm assuming you know how to factor a 2nd degree polynomial. If you need help with that, write me a note.
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So,
or , BUT remember that 5 was excluded from the domain, therefore the only solution is
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Hope this helps
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In the graph below, note the curve is asymptotic to the y-axis and there is a discontinuity at 5.

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