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How do you add or subtract #(x^2)/(x-1)-(1)/(x-1)#?

Answer 1

Avery Alexander

When you have fractions that have the same denominator, you simply add/subtract the numerators.

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

But note that if we check the roots for the numerator, we'll end up factoring it:

#x^2-1=0# #x^2=1# #x=+-1# => #(x+1)(x-1)#

Rewriting:

#((x+1)cancel(x-1))/cancel(x-1)#

Thus, your final answer for this subtraction is #x+1#

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Answer 2

Eva Abramson

To add or subtract fractions with the same denominator, you simply combine the numerators and keep the common denominator. In this case, the common denominator is (x-1).

So, to add or subtract (x^2)/(x-1) - (1)/(x-1), you can combine the numerators and keep the denominator:

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

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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.