sqrt(x^2 - 5x + 3) = sqrt (x^2 + 4x -1) solve for x

To solve sqrt(x^2-5x+3) =
sqrt(x^2+4x-1).

We rearrange this
as:

sqrt(x^2-5x+3) -sqrt(x^2+4x-1) =
0.

We rationalise te
numerator:

{sqrt(x^2-5x+3)-sqrt(x^2+4x-1}{sqrt(x^2-5x+3)+sqrt(x^2+4x+1}/{sqrt(x^2-5x+3)+sqrt(x^2+4x-1}
= 0

 (-5x+3-4x-1)/{sqrt(x^2-5x+3)+sqrt(x^2+4x-1} =
0

Multiply both sides by {sqrt(x^2-5x+3)+sqrt(x^2+4x-1} and
we get:

 -5x+3-4x+1 = 0

-9x+4
= 0.

-9x= -4

x = -2/-9 =
2/9.

Therefor x = 4/9 is the
solution.