Question

А) а/a-b + 3a/a+b-2ab/a2-b2

Answer 1

Решение во вложении
..................................

Answer 2

To simplify the expression (a/a-b) + (3a/a+b-2ab/a^2-b^2), we need to find a common denominator and combine the fractions.

First, let's find the common denominator for the three fractions. The denominators are a-b, a+b-2ab, and a^2-b^2.

The common denominator for these three fractions is (a-b)(a+b-2ab)(a+b).

Now, let's rewrite each fraction with the common denominator:

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

Now we can combine the fractions:

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

To simplify further, we can cancel out common factors:

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

Expanding and simplifying the numerator:

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

Combining like terms:

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

Simplifying further:

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

Combining like terms:

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

So, the simplified expression is: (a^3+b^3+ab^2+a^2+b^2) / [(a-b)(a+b)(a+b-2ab)]