Question

A³b-ab³/2b-a*a+2b/a⁴-b⁴

Answer 1

Ответ:

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

Answer 2

To simplify the expression (A³B - AB³) / (2B - A) * (A + 2B) / (A⁴ - B⁴), we'll first factor the numerator and denominator:

Numerator (A³B - AB³): Factor out AB: AB(A² - B²) Factor the difference of squares: AB(A + B)(A - B)

Denominator (A⁴ - B⁴): Factor the difference of squares: (A² - B²)(A² + B²) Factor again: (A + B)(A - B)(A² + B²)

Now the entire expression becomes:

AB(A + B)(A - B) / (2B - A) * (A + 2B) / (A + B)(A - B)(A² + B²)

Now we can cancel out common terms in the numerator and denominator:

(A + B) and (A - B) cancel out in the numerator and denominator.

The simplified expression is:

AB / (2B - A) * (A + 2B) / (A² + B²)

Please note that if any of the factors (A + B), (A - B), or (A² + B²) are equal to zero, then the expression would be undefined, as division by zero is not allowed.