Question 75030
To make a fraction of {{{18/(x-3)}}} just place 18/(x-3) in triple curly brackets.
 {{{ 18/(x-3) = x/3 }}} Start with the given problem
 {{{ (3/1)(18/(x-3)) = (x/cross(3))(cross(3)/1)}}}Multiply both sides by 3, this eliminates the denominator of the right side
{{{cross(x-3)(54/cross(x-3))=x(x-3)}}}Multiply both sides by (x-3), this eliminates the denominator of the left side
So we're left with this:
{{{54=x(x-3)}}}
{{{54=x^2-3x)}}}Distribute the x
{{{0=x^2-3x-54)}}}Subtract 54 from both sides
{{{0=(x-9)(x+6)}}}Factor the right side
{{{x-9=0}}}
{{{x=9}}}There's one answer
{{{x+6=0}}}
{{{x=-6}}}There's the other answer
So the solution is x=9 and x=-6
<p>
Check:
 {{{ 18/(x-3) = x/3 }}}Plug in x=9
{{{ 18/(9-3) = 9/3 }}}
{{{ 18/6 = 3 }}}
{{{ 3= 3 }}}works
{{{ 18/(x-3) = x/3 }}}Plug in x=-6
{{{ 18/((-6)-3) = -6/3 }}}
{{{ 18/(-9) = -2 }}}
{{{ -2= -2 }}}works

Here's another way to solve it:
When you have the quadratic {{{0=x^2-3x-54)}}}, plug the coefficients into the quadratic formula:
*[invoke quadratic "x", 1, -3, -54 ]
And you see the same answer, but it's just another way to get there.