Question 110624
{{{3/x+3/(x-5)=(3x-12)/(x-5)}}}
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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 {{{x}}} and {{{x-5}}}, so the only common denominator is {{{x(x-5)}}}.
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{{{3(x-5)/x(x-5)+3x/x(x-5)=x(3x-12)/x(x-5)}}}
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Now we need to simplify and collect like terms.
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{{{(3x-15+3x)/x(x-5)=(3x^2-12x)/x(x-5)}}}
{{{(3x-15+3x)=(3x^2-12x)}}}, after multiplication by {{{x(x-5)}}}
{{{6x-15-3x^2+12x=0}}}
{{{3x^2-18x+15=0}}}, after collecting terms and multiplying by -1
{{{x^2-6x+5=0}}}, after dividing by 3
{{{(x-5)(x-1)=0}}}, 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,
{{{x=5}}} or {{{x=1}}}, BUT remember that 5 was excluded from the domain, therefore the only solution is {{{x=1}}} 
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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.
{{{graph(400,400,-10,10,-10,10,3/x+3/(x-5)-(3x-12)/(x-5))}}}