Question 316314
{{{3/(u-2)=-4-5/(u-3)}}}
Use a common denominator, {{{(u-2)(u-3)}}}
{{{3(u-3)/((u-2)(u-3))=(-4(u-2)(u-3))/((u-2)(u-3))-5(u-2)/((u-2)(u-3))}}}
{{{(3u-9)/((u-2)(u-3))=-4(u^2-5u+6)/((u-2)(u-3))-(5u-10)/((u-2)(u-3))}}}
{{{3u-9=-4u^2+20u-24-5u+10}}}
{{{-4u^2+12u-5=0}}}
{{{4u^2-12u+5=0}}}
{{{(2u-1)(2u-5)=0}}}
Two solutions:
{{{2u-1=0}}}
{{{2u=1}}}
{{{highlight( u=1/2)}}}
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{{{2u-5=0}}}
{{{2u=5}}}
{{{highlight(u=5/2)}}}
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Verify that the solutions work by plugging them back into the original equation.