Question 356367
{{{(x-1)/(x+3)=2}}}
Use the common denominator {{{x+3}}}
{{{(x-1)/(x+3)=(2(x+3))/(x+3)}}}
{{{(x-1)/(x+3)-(2(x+3))/(x+3)=0}}}
{{{(x-1-2(x+3))/(x+3)=0}}}
{{{(x-1-2x-6))/(x+3)=0}}}
{{{(-x-7)/(x+3)=0}}}
{{{-(x+7)/(x+3)=0}}}
The expression equals zero only when,
{{{x+7=0}}}
{{{highlight(x=-7)}}}
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Graphical verification of the solution:
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{{{drawing(300,300,-8,2,-2,8,grid(1),circle(-7,2,0.15),graph(300,300,-8,2,-2,8,(x-1)/(x+3),2))}}}