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Add Rational Expression

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Add Rational Expression SHOW STEPS-example-1

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Answer:


(5x^2-10x+1)/(x^2-4)

Explanation:

Given rational expression:


(5x)/(x+2)+(1)/(x^2-4)

To add two fractions, they must share a common denominator.

In this case, we start by factoring the denominator of the second fraction using the difference of two squares formula, a² - b² = (a + b)(a - b):


(5x)/(x+2)+(1)/((x+2)(x-2))

To ensure both fractions have the same denominator, we multiply the numerator and denominator of the first fraction by (x - 2):


(5x(x-2))/((x+2)(x-2))+(1)/((x+2)(x-2))

Now that both fractions share the same denominator, we can combine them by adding their numerators:


(5x(x-2)+1)/((x+2)(x-2))

Finally, simplify the numerator and denominator:


(5x^2-10x+1)/(x^2-4)

Therefore, the simplified rational expression is:


\large\boxed{\boxed{(5x^2-10x+1)/(x^2-4)}}

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