5x/(x^2-9)+2/(x+4)

Question

I'm in AlegebraII and im on Adding  and Subtracting Rational Expressions

Answer 1

Look at this like you were finding a common denominator:

The common denominator would be (x² - 9)(x + 4). So we need to multiply the first term by (x+4)/(x+4) and the second by (x² - 9)/(x² - 9) to get^:

5x(x + 4)/[(x² - 9)(x + 4)] + 2(x² - 9)/[(x² - 9)(x + 4)]

With a common denominator, we can combine our numerators into one:

[5x² + 20x + 2x² - 18]/[(x² - 9)(x + 4)]

[7x² + 20x - 18]/[(x² - 9)(x + 4)]

On inspection, I don't think you can simplify the numerator, but you can always test it with the quadratic formula.