does anyone know how to simplify a^2 - ab + ab^2/a^2 - b^2 + ab^2 + b^3?

a² - ab + ab²
= a(a - b - b²)

a² - b² + ab² + b³
= (a² - b²) + (ab² + b³)
= (a - b)(a + b) + b²(a + b)
= (a + b)[(a - b) - b²]
= (a + b)(a - b - b²)

Hence, (a² - ab + ab²) / (a² - b² + ab² + b³)
= a(a - b - b²) / (a + b)(a - b - b²)
= a / (a + b)

assuming expression is

a^2 - ab + ab^2/a^2 - b^2 + ab^2 + b^3

a^2 - ab + a^-1b^2 - b^2 + ab^2 + b^3



you can see why this doesn't make 100% sense; you need to be sure to use brackets to clearly indicate where the division is.

(a^2 - ab + ab^2) / (a^2 - b^2 + ab^2 + b^3)
= a(a - b + b^2) / ((a + b)(a - b) + b^2(a + b))
= a(a - b + b^2) / (a + b)((a - b + b^2))
= a(a - b + b^2) / (a + b)(a + (b - 1) b)
= a(a - b + b^2) / (a + b) (a + b^2 - b)
= a(a - b + b^2) / (a + b) (a - b + b^2)
= a / (a + b)