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`@Wan`

`a) (2x^2-x)/(x-1) + (x+1)/(1-x) + (2-x^2)/(x-1) (x\ne1)`

`= (2x^2 - x - x - 1 + 2-x^2)/(x-1)`

`= (x^2 -2x +1)/(x-1)` 

`= [(x-1)^2]/(x-1)`

`= x-1` 

~~~~~~~~~~~~~~~~~~~~~~

`e) (x^2-36)/(2x+10) . 3/(6-x) (x\ne - 5 ; x \ne 6) `

`= [(x-6)(x+6)]/(2x+10) . (-3)/(x-6)`

`= [-3(x+6)]/(2x+10)`

`= (-3x-18)/(2x+10)`

~~~~~~~~~~~~~~~~~~~~~~~~~~

`b) (3x+5)/(x^2-5x) + (25-x)/(25-5x) (x\ne 0 ; x \ne5) `

`= (3x+5)/[x(x-5)] + (25-x)/[5(5-x)]`

`= (3x+5)/[x(x-5)] + [-(25-x)]/[5(x-5)]`

`= [5(3x+5) - x(25-x)/[5x(x-5)]`

`= (x^2-10x+25)/[5x(x-5)]`

`= [(x-5)^2]/[5x(x-5)]`

`= (x-5)/(5x)` 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`(5x-10)/(x^2+7) : (2x-4) (x \ne2)`

`= [5(x-2)]/(x^2+7) . 1/[2(x-2)]`

`= 5/[2(x^2+7)]`

`=5/(2x^2+14)`