Question 289126
{{{sqrt(3)+sqrt(x-2)=sqrt(x+3)}}} Start with the given equation.



{{{(sqrt(3)+sqrt(x-2))^2=x+3}}} Square both sides (to eliminate the square root on the right side)



{{{3+2*sqrt(3)*sqrt(x-2)+x-2=x+3}}} FOIL



{{{3+2*sqrt(3(x-2))+x-2=x+3}}} Combine the roots.



{{{2*sqrt(3x-6)+x+1=x+3}}} Distribute



{{{2*sqrt(3x-6)=x+3-x-1}}} Subtract 'x' from both sides. Subtract 1 from both sides.



{{{2*sqrt(3x-6)=2}}} Combine like terms.



{{{sqrt(3x-6)=2/2}}} Divide both sides by 2.



{{{sqrt(3x-6)=1}}} Reduce.



{{{3x-6=1^2}}} Square both sides (to eliminate the square root)



{{{3x-6=1}}} Square 1 to get 1.



{{{3x=1+6}}} Add 6 to both sides.



{{{3x=7}}} Combine like terms.



{{{x=7/3}}} Divide both sides by 3 to isolate 'x'.



So the solution is {{{x=7/3}}}



I'll let you do the check. Simply plug this value back into the equation and simplify. You should get an equation that is always true.