Question 16273
Solve for x:

{{{(x - 1)/(2x + 1) = (x + 1)/(x - 1)}}} Cross-multiply.
{{{(x - 1)(x - 1) = (x + 1)(2x + 1)}}} Perform the indicated multiplication on both sides.
{{{x^2 - 2x + 1 = 2x^2 + 3x + 1}}} Subtract x^2 from both sides.
{{{-2x + 1 = x^2 + 3x + 1}}} Add 2x to both sides.
{{{1 = x^2 + 5x + 1}}} Subtract 1 from both sides.
{{{0 = x^2 + 5x}}} Factor an x on the right side.
{{{0 = x(x + 5)}}} App;y the zero products principle.

{{{x = 0}}} and/or {{{x + 5 = 0}}}
If {{{x + 5 = 0}}}, then {{{x = -5}}}

The two roots are:

x = 0
x = -5

Finally:
The smaller number is -5
The larger number is 0