Simplify: (x^2-x+6)/(x-3) How would you write this out?

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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The expression `(x^2 - x +6)/(x-3)` cannot actually be simplified. Normally, when factorizing you would first establish if it can be factorized by using the factors of the first term (x times x) and the factors of the third term (1 x 6 OR 3 x 2). 1x6 would clearly NOT work as the factors cannot render a middle term of -1 (that is, the co-efficient of middle term (ie the -x). Although the factors (3 x 2) look as if they work as they will render a middle term of   -x, they will NOT render a +6 at the end:

`(x-3)(x+2)` = `x^2 +2x-3x-6` = `x^2 - x -6` . If this was the expression then the (x-3) would cancel with the denominator leaving a simplified answer of (x+2)

Using the formula will not work either as it produces an imaginary number as the number inside the square root will be a negative number preventing simplification of this expression. The final answer to this particular question is the same as you started with:

`(x^2 - x+6)/(x-3)`

 

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