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# To simplify a rational expression

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In regards to the example that I included, can we cancel out the x's?
I guess the big question here is how to we identify whether we are dealing with factors or with terms?

Answer: When simplifying the rational expression, it is improper to cancel out the x's in general. For instance, (x^2-x)/(x^2+x+1). We cannot cancel x on both sides to be (x-1)/(x+1+1). The reason is the numerator has x as a factor, but the denominator does not.

To simplify a rational expression, we need to factor both numerator and denominator. Then cancel out the common factor(s).

https://brainmass.com/math/basic-algebra/simplifying-rational-expression-example-problem-495604

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To simplify a rational expression, we always need to factor both numerator and denominator first. Then we need to see if both numerator and denominator have common factor(s). If they do, then we can cancel out them to simplify the expression. If not, then the expression cannot be simplified.

For this example (x^2-x)/(x^2+x+1), although the numerator (x^2-x) can be factored out to be x(x-1), the denominator x^2+x+1 can not be factored further. Hence, this rational expression cannot be simplified.

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