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How do you simplify #(x^3+5x^2-x-5)/(x^2-25)*(x+1)#?

Answer 1

Eva Abramson

#((x+1)^2(x-1))/((x-5))#

Factorise

#(x^3+5x^2color(red)(-x-5))/(x^2-25)xx(x+1)/1 #

=# (x^2(x+5)color(red)(-(x+5)))/((x+5)(x-5)) xx (x+1)/1#

=# ((x+5)(x^2-1))/((x+5)(x-5)) xx (x+1)/1#

=# (cancel((x+5))(x+1)(x-1))/(cancel((x+5))(x-5)) xx (x+1)/1#

=#((x+1)^2(x-1))/((x-5))#

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Answer 2

Hazel Anglin

To simplify the expression (x^3+5x^2-x-5)/(x^2-25)*(x+1), we can factor the numerator and denominator. The numerator can be factored as (x+1)(x^2-5), and the denominator can be factored as (x-5)(x+5).

Now, we can cancel out the common factors between the numerator and denominator. The (x+1) term cancels out, leaving us with (x^2-5)/(x-5)(x+5).

Therefore, the simplified expression is (x^2-5)/(x-5)(x+5).

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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.