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How do you simplify #x/ (x^2 - 4) - 2/(x - 2)#?

Answer 1

Eli Assouline

= #(-1(x +4))/((x-2)(x+2))#

#x/(x^2 - 4) - 2/(x-2)# can be written as

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

= #x/((x - 2)(x+2)) - (2(x+2))/((x-2)(x+2))#

= #(x - 2(x+2))/((x-2)(x+2))#

= #(x - 2x - 4)/((x-2)(x+2))#

= #(-x - 4)/((x-2)(x+2))#

= #(-1(x +4))/((x-2)(x+2))#

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Answer 2

Eva Adamson

To simplify the expression x/ (x^2 - 4) - 2/(x - 2), we need to find a common denominator and combine the fractions. The common denominator is (x - 2)(x + 2).

Multiplying the first fraction by (x + 2)/(x + 2), and the second fraction by (x + 2)/(x + 2), we get:

(x(x + 2))/((x - 2)(x + 2)) - 2(x + 2)/((x - 2)(x + 2))

Expanding and combining the numerators, we have:

(x^2 + 2x - 2x - 4 - 2x - 4)/((x - 2)(x + 2))

Simplifying the numerator, we get:

(x^2 - 8)/((x - 2)(x + 2))

Therefore, the simplified expression is (x^2 - 8)/((x - 2)(x + 2)).

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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.