Question 944263
{{{sqrt(3x+1)-sqrt(x-1)=2}}}
{{{sqrt(3x+1)=sqrt(x-1)+2}}}
{{{3x+1=x-1+4sqrt(x-1)+4}}}
{{{2x-2=4sqrt(x-1)}}}
{{{2(x-1)=4sqrt(x-1)}}}
{{{x-1=2sqrt(x-1)}}}
{{{x^2-2x+1=4x-4}}}
{{{x^2-6x+5=0}}}
{{{(x-1)(x-5)=0}}}
.
.
.
{{{x-1=0}}}
{{{x=1}}}
and
{{{x-5=0}}}
{{{x=5}}}
Now verify the solution in the original equation to make sure there are not false solutions.