Reduce the rational expression to lowest terms.? Best answers rewarded!!?

Question

(a^3+27b^3)/(a^2-9b^2)

Answer 1

The rational expression (a³ + 27b³)/(a² - 9b²)

= [a³ + (3b)³]/[a² - (3b)²]

Apply the formula a³ + b³ = (a + b)(a²  - ab + b²)

= [(a + 3b)(a²  - 3ab + (3b)²]/[a² - (3b)²

Apply the formula a² - b² = (a + b)(a - b)

= [(a + 3b)(a²  - 3ab + (3b)²]/[(a + 3b)(a - 3b)]

= [(a²  - 3ab + 9b²]/(a - 3b)

(a³ + 27b³)/(a² - 9b²) = [(a²  - 3ab + 9b²]/(a - 3b).