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How do you simplify # (5x - 25) / (x^2 - 25) # and what are the restrictions?

Answer 1

Eva Abramson

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

#=(5(x-5))/{(x+5)(x-5)}#

#=5/((x+5))*((x-5))/((x-5))#

#=5/((x+5))*1#

#=5/(x+5)#

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Answer 2

Eva Abramson

To simplify the expression (5x - 25) / (x^2 - 25), we can factor the numerator and denominator. The numerator can be factored as 5(x - 5), and the denominator can be factored as (x - 5)(x + 5).

By canceling out the common factor of (x - 5), we get the simplified expression of 5 / (x + 5).

The restrictions for this expression are that x cannot be equal to 5 or -5, as these values would result in division by 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.