4x^4-13x^2+9=0

2x-square root of x-1=0

3/x+4/(x+1)=2

(x^2 -1)(4x^2 -9) = 0

(x+1)(x-1)(2x+3)(2x-3) = 0
Take it from there.

(sqrtx -1)(2sqrtx +1) = 0
Ditto.

Your last equation needs parentheses for clarification