What is the result of fractions sumation 2x/(x^2-4)-3/(x-2)(x+2)+2/(x+2) ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We need the result of : 2x/(x^2-4)-3/(x-2)(x+2)+2/(x+2)

2x/(x^2-4)-3/(x-2)(x+2)+2/(x+2)

first make the denominator the same for all the terms

=> 2x/(x -2)(x + 2) - 3/(x-2)(x+2) + 2(x - 2)/(x+2)(x - 2)

=> [2x - 3 + 2(x - 2)]/(x - 2)(x + 2)

=> [2x - 3 + 2x - 4]/(x - 2)(x + 2)

=> (4x - 7)/(x - 2)(x + 2)

The result is (4x - 7)/(x - 2)(x + 2)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We notice that  the ratios don't have the same denominator.

We'll calculate the least common denominator:

LCD = (x-2)(x+2)

LCD = x^2 - 4 (that is the denominator of the first and 2nd ratios)

We'll multiply the 3rd fraction by (x-2):

(2x - 3 + 2x - 4)/(x^2-4)

We'll  combine like terms and we'll get:

(4x - 7)/(x^2-4)

The result of adding the given fractions is (4x - 7)/(x^2-4).

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