Hi i need some help please on how to solve these problems. i tried each one but either cant figure out the answer/ i got an answer but im not sure if its correct.

3) Factor completely. x - x^1/2 -6

here i changed the -x^1/2 into square root x since the two mean the same thing. so then i had.

x-(squareroot x) -6. i then to kill the square root i rooted the whole problem so then it came out to be.

x^2+x-36 then from here i can factor it out... so im thinking this is the answer since

(x+6)(x-6) wotn work or even changing it out with 9 and 4 or 18 and 2... if you know what i mean...i could complete the square but then again im factoring it out not solving for x so like i said im not sure if that is the answer....

4) ok last one( the one i cant seem to solve)

$\displaystyle \displaystyle{\frac{1}{2}}+\displaystyle{\frac{1}{ x-3}}=\displaystyle{\frac{x-2}{x-3}}$

so i tried this problem about 6 diffrent ways and ended up with ansers like 3,2,4,9,7 and when i plug them in they dont equal out..... i tell you one way i tried this..

i put everything on one side. then made it so each fraction had the same denominator so i got.

-3+1-x-2/x-3 -> -4-x / x-3

from here i think i loose it and i multiply the top and bottom by (x-3) and end up getting

-(x^2+2x-12) / x^2-6x+9 i try to factor this out but only the bottom i can factor out and not the top...

help would be much appreciated! thanks!