Question 63024
Solve. Write all apparent solutions. Cross out those that are extraneous

{{{sqrt(u-3)-sqrt(u)=3}}}
{{{sqrt(u-3)-sqrt(u)+sqrt(u)=sqrt(u)+3}}}
{{{sqrt(u-3)=sqrt(u)+3}}}
{{{(sqrt(u-3))^2=(sqrt(u)+3)^2}}}
{{{u-3=(sqrt(u)+3)(sqrt(u)+3)}}}
{{{u-3=sqrt(u)(sqrt(u)+3)+3(sqrt(u)+3)}}}
{{{u-3=sqrt(u^2)+3sqrt(u)+3sqrt(u)+9}}}
{{{u-3=u+6sqrt(u)+9}}}
{{{u-u-3-9=u-u+6sqrt(u)+9-9}}}
{{{-12=6sqrt(u)}}}
{{{-12/6=6sqrt(u)/6}}}
{{{-2=sqrt(u)}}}
{{{(-2)^2=(sqrt(u))^2}}}
{{{4=u}}}  Check to see if it's extraneous.
{{{sqrt(4-3)-sqrt(4)=3}}}
{{{sqrt(1)-2=3}}}  
{{{1-2=3}}}
{{{-1=3}}}  This is not true, u=4 is extraneous, there is no soltuion.
Happy Calculating!!!