Solve for `x`:`1/ ((x -1)(x -2))+1/( (x-2)(x-3))=2/ 3', `x is not equal to 1,2,3 .

Explanation

In the given figure area of semicircle having AD`=(pir^2)/2=pi(4.5)^2/2`

Area of circle having diameter`=4.5cm`

`=pi(4.5/2)^2`

Area of semicircle having AB as diameter`=pi/2*(3/2)^2`

Area of shaded region`=` Area of part 1 `+` Area of third part - Area of second portion - Area of third portion - Area of fifth portion

Area of first part - Area of second part - Area of fifth part

`=pi/2[(4.5)^2-(4.5)^2/2-9/4]`

`=pi*3.9375cm^2`