Question

Выполните действие 4/a+2-3/a-2+12/a^2-4

Answer 1

Решение смотри на фотографии

Answer 2

Calculation of the Expression

To solve the given expression 4/a + 2-3/a-2 + 12/a^2-4, we can follow these steps:

1. Factor the denominators of the fractions. 2. Find the least common denominator. 3. Combine the fractions and simplify the expression.

Factoring the Denominators

The expression contains fractions with denominators that can be factored. The denominators are a, a-2, and a^2-4.

The factorization of a^2-4 is (a+2)(a-2).

Finding the Least Common Denominator

The least common denominator for the fractions in the expression is the product of the distinct factors in the denominators. Therefore, the least common denominator is a(a-2)(a+2).

Combining the Fractions

Now, we can rewrite the expression using the least common denominator and combine the fractions.

The expression becomes: (4(a-2) + 2(a)(a+2) - 3(a)(a+2) + 12) / (a(a-2)(a+2)).

Simplifying the expression further, we get: (4a - 8 + 2a^2 + 4a - 3a^2 - 6a + 12) / (a(a-2)(a+2)).

Combining like terms, the expression simplifies to: (-a^2 + 5a + 4) / (a(a-2)(a+2)).

Therefore, the simplified form of the given expression 4/a + 2-3/a-2 + 12/a^2-4 is (-a^2 + 5a + 4) / (a(a-2)(a+2)).