Question 828275
<pre>
{{{x}}}{{{""=""}}}{{{y + sqrt(y^2+1)}}}

Isolate the square root term:

{{{x-y}}}{{{""=""}}}{{{sqrt(y^2+1)}}}

Square both sides:

{{{(x-y)^2}}}{{{""=""}}}{{{(sqrt(y^2+1))^2}}}

Squaring a square root takes away the square root

{{{(x-y)^2}}}{{{""=""}}}{{{y^2+1}}}

Write the left sides as {{{(x-y)(x-y)}}}

{{{(x-y)(x-y)}}}{{{""=""}}}{{{y^2+1}}}

Use FOIL

{{{x^2-2xy+y^2}}}{{{""=""}}}{{{y^2+1}}}

Subtract {{{y^2}}} from both sides:

{{{x^2-2xy}}}{{{""=""}}}{{{1}}}

Isolate the term that contains y, which is -2xy.
Since it's negative on the left, we isolate it
on the right:

{{{x^2-1}}}{{{""=""}}}{{{2xy}}}

Divide both sides by 2x

{{{(x^2-1)/(2x)}}}{{{""=""}}}{{{(2xy)/(2x)}}}

{{{(x^2-1)/(2x)}}}{{{""=""}}}{{{(cross(2x)y)/(cross(2x))}}}

{{{(x^2-1)/(2x)}}}{{{""=""}}}{{{y}}}

{{{y}}}{{{""=""}}}{{{(x^2-1)/(2x)}}}

Edwin</pre>