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

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Answer 1 · 2015-05-22T13:23:08

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#