What is `f (x)-1/(x+1)+1/(x+2)` if `f(x)=1/((x+1)(x+2))` ?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`f(x) = 1/((x+1)(x+2))`

`f(x)-1/(x+1)+1/(x+2)`

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

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

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

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

`= 0`

So the answer is `f(x)-1/(x+1)+1/(x+2) = 0`

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