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How do you simplify rational equations #[a / (a+1)] - [1 / (a-1)]#?

Answer 1

Abigail Allen

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

We have: #[(a) / (a + 1)] - [(1) / (a - 1)]#

Let's combine the fractions:

#= ((a) (a - 1) - (1) (a + 1)) / ((a + 1) (a - 1))#

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

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

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Answer 2

Avery Alexander

To simplify the rational equation [a / (a+1)] - [1 / (a-1)], you need to find a common denominator for the two fractions. The common denominator in this case is (a+1)(a-1).

Next, multiply the numerator and denominator of the first fraction, a, by (a-1), and multiply the numerator and denominator of the second fraction, 1, by (a+1).

This will give you (a(a-1) / (a+1)(a-1)) - ((a+1) / (a+1)(a-1)).

Now, simplify the equation by combining the numerators over the common denominator: (a(a-1) - (a+1)) / (a+1)(a-1).

Expanding the equation further, you get (a^2 - a - a - 1) / (a+1)(a-1).

Combine like terms in the numerator: (a^2 - 2a - 1) / (a+1)(a-1).

This is the simplified form of the rational equation [a / (a+1)] - [1 / (a-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.