Question

solve for x please answer urgent from the pic

Answer 1

cubic ::::3 roots are 0,2,-2

Answer 2

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

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

Multiplying out,
3(x-3+x-1)=2(x-1)(x-2)(x-3)

6x-12=2(x³-6x²+11x-6)

3x-6=x³-6x²+11x-6

x³-6x²+8x=0

x(x²-6x+8)=0

x=0
one root of x is 0

Again solving this x²-6x+8=0 quadratic equation
x= (-b ±√(b²-4ac))/2a
here, b= -6, a=1, c=8

x= 6±√(36-4×1×8)/2×1=(6±√4)/2

x=(6+2)/2=4,
2nd root of x is 4

x=(6-2)/2=2,
3rd root of x is 2.
But it's given that x≠2

So, Roots of x are (0, 4)