Question 117831
{{{7/(x) - 1/(x-3) = 9/(x^2-3x)}}} Start with the given expression




{{{7/(x) - 1/(x-3) = 9/(x(x-3))}}} Factor {{{x^2-3x}}}



{{{((x)(x-3))(7/(x) - 1/(x-3) )=((x)(x-3))( 9/(x(x-3)))}}} Multiply both sides by the LCD {{{(x)(x-3)}}}





{{{7(x-3) - x=9}}} Distribute and multiply



{{{7x-21-x=9}}} Distribute again



{{{6x-21=9}}} Combine like terms on the left side



{{{6x=9+21}}}Add 21 to both sides



{{{6x=30}}} Combine like terms on the right side



{{{x=(30)/(6)}}} Divide both sides by 6 to isolate x




{{{x=5}}} Divide


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Answer:

So our answer is {{{x=5}}}