Question 70721
{{{(x-9)/(x+4)=3}}}
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Start by getting rid of the denominator {{{x+4)}}} on the left side.  Do this by the means
of multiplying both sides of this equation by {{{x+4}}}.  When you do the equation becomes:
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{{{(x+4)*(x-9)/(x+4)= 3*(x+4)}}}
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Notice on the left side that the denominator and numerator both contain {{{x+4}}} and they 
can be canceled because {{{(x+4)/(x+4) = 1}}}. After that cancellation, the left side is 
just {{{x-9}}}.  The right side can be multiplied out.  When it is, the resulting product is
{{{3x + 12}}}.  This makes the equation:
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{{{x-9 = 3x + 12}}}
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Get rid of the 9 on the left side by adding +9 to both sides of the equation.  On the left
side the +9 cancels with the -9 and you are just left with x.  On the right side the +9
combines with the +12 to become 21. So the right side is {{{3x+21}}} and the equation is:
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{{{x = 3x + 21}}}
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Remove the 3x from the right side by adding -3x to both sides.  On the right side, the
-3x cancels the +31 and you are left with just +21.  On the left side the -3x adds to
the +x and the result is -2x.  Now the equation has been reduced to:
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{{{-2x = 21}}}
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To solve for x just divide both sides by -2.  The left side becomes just x and the right
side becomes {{{-21/2 = -10.5}}}.  This makes the answer to the problem:
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{{{x = -10.5}}}
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Hope this gives you some insight into the problem.  Denominators can be removed by finding
a way to multiply them out of existence.