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How do you combine #x^2/(x-1) - 1/(x-1)#?

Answer 1

You do it by using the lowest common denominator among both fractions.

However, when both fractions have the same denominator and you're working with sums or subtractions, you can just go directly to the operation, summing/subtracting the terms in the numerators, keeping the denominator as it is, as follows:

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

Note that the numerator #x^2-1# has two roots, which we can find by isolating #x#:

#x^2=1# #x=sqrt(1)# #x=1# and #x=-1#, which is the same as if we wrote: #x-1=0# and #x+1=0#.

By factoring #x^2-1# using its two roots, we can have your answer like this:

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

So, your final answer is #x+1#

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Answer 2

Isaiah Anthony

Since the numerators are the same:

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

Now #x^2 - 1 = (x+1)(x-1)#

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

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Answer 3

Savannah Anderson

To combine the expressions x^2/(x-1) and -1/(x-1), we need a common denominator. In this case, the common denominator is (x-1).

To combine the fractions, we can subtract the numerators and keep the common denominator.

Therefore, the combined expression is (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.