Square of Difference: Equations with variables on both sides

Solve the following equation:

$\sqrt{x-1}\times\sqrt{x-2}=x-3$

$x=\frac{7}{3}$

$\frac{(\frac{1}{x}-\frac{1}{2})^2}{(\frac{1}{x}-\frac{1}{3})^2}=\frac{9}{4}$

Find X

2.5

Solve the following equation:

$\frac{x^3+1}{(x-1)^2}=x+4$

$x=3,\frac{1}{2}$

Solve the following equation:

$(x-4)^2+3x^2=-16x+12$

$x=-1$

Solve the following equation:

$(x-5)^2-5=10+2x$

$x_1=6+\frac{\sqrt{104}}{2},\\x_2=6-\frac{\sqrt{104}}{2}$

Solve the following equation:

$(x-5)^2-5=-12+2x$

$x_1=8,x_2=4$

Solve the following equation:

$\frac{(2x-1)^2}{x-2}+\frac{(x-2)^2}{2x-1}=4.5x$

$$$-1\pm\sqrt{3}$