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How do you simplify #(2x-10)/(25-x^2)# and what are the excluded values for the variables?

Answer 1

Nathan Axel

Given: #(2x-10)/(25-x^2)#

Factor out -2:

#(-2(x-5))/(x^2-25)#

Factor the denominator:

#(-2(x-5))/((x-5)(x+5))#

Please observe the canceled factors:

#(-2(cancel(x-5)))/((cancel(x-5))(x+5))#

Remove the canceled factors and append the excluded value:

#(-2)/(x+5); x!=-5#

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Answer 2

Julia Adams

To simplify (2x-10)/(25-x^2), we can factor the denominator as the difference of squares: (5-x)(5+x). Then, we can cancel out the common factor of (5-x) in the numerator and denominator. The simplified expression is (2x-10)/(5+x).

The excluded values for the variables are the values that make the denominator equal to zero. In this case, the excluded value is x = 5, since it would make the denominator (5-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.