Question

Упростите выражение:
$\frac{a^{3}-27b^3 }{a^3+3a^2b+9ab^2}$

Answer 1

Здравствуйте!

Ответ:

$\displaystyle \frac{a - 3b}{a}$

Объяснение:

$\displaystyle a {}^{3} - b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} )$

$\displaystyle \frac{a^{3}-27b^3 }{a^3+3a^2b+9ab^2} = \\ \\ = \frac{(a - 3b)(a {}^{2} + 3ab + b {}^{2} )}{a(a {}^{2} + 3ab + b {}^{2} )} = \\ \\ = \frac{a - 3b}{a}$