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How do you simplify and find the excluded value of #(x^2+x+1)/(1-x^2)#?

Answer 1

see explanation.

Factorise the denominator using the #color(blue)"difference of squares"#

#(x^2+x+1)/((1-x)(1+x))#

The denominator of the function cannot equal zero as this would make it #color(blue)"undefined".#Equating the denominator to zero and solving gives the values that x cannot be.

#"solve " (1-x)(1+x)=0#

#rArrx=1" or " x=-1larrcolor(red)" excluded values"#

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Answer 2

Nathan Axel

To simplify the expression (x^2+x+1)/(1-x^2), we can factor the numerator and denominator. The numerator cannot be factored further, but the denominator can be factored as (1-x)(1+x).

Next, we can cancel out common factors between the numerator and denominator. In this case, there are no common factors to cancel out.

Therefore, the simplified expression is (x^2+x+1)/(1-x)(1+x).

To find the excluded values, we need to identify the values of x that would make the denominator equal to zero. In this case, the excluded values are x = -1 and x = 1, since they would make the denominator (1-x)(1+x) equal to zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.