Question 1024879
<pre>
{{{sqrt(a-1)}}}{{{""=""}}}{{{a-3}}}

Square both sides:

{{{(sqrt(a-1))^2}}}{{{""=""}}}{{{(a-3)^2}}}

{{{a-1}}}{{{""=""}}}{{{a^2-6a+9}}}

{{{0}}}{{{""=""}}}{{{a^2-7a+10}}}

{{{0}}}{{{""=""}}}{{{(a-5)(a-2)}}}

{{{(a-5)(a-2)}}}{{{""=""}}}{{{0}}}

a-5 = 0;   a-2 = 0
  a = 5;     a = 2

Test each in the original equation to test
for extraneous answers:

Test a = 5:

{{{sqrt(a-1)}}}{{{""=""}}}{{{a-3}}}
{{{sqrt(5-1)}}}{{{""=""}}}{{{5-3}}}
{{{sqrt(4)}}}{{{""=""}}}{{{2}}}
{{{2}}}{{{""=""}}}{{{2}}}    

a = 5 is a solution.

Test a = 2:

{{{sqrt(a-1)}}}{{{""=""}}}{{{a-3}}}
{{{sqrt(2-1)}}}{{{""=""}}}{{{2-3}}}
{{{sqrt(1)}}}{{{""=""}}}{{{-1}}}
{{{1}}}{{{""=""}}}{{{-1}}}    

a = 2 is not a solution.

Answer: a = 5

Edwin</pre>