Question

Add Rational Expression

SHOW STEPS

Answer 1

`(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)}}`