Question

Упростите выражение (4a/(дробь)4-a^2-a-2/(дробь)4+2a)*4/(дробь)a+2-a/(дробь) 2-a Ещё пример Вычислите (5,2:2-4,8^2)*(16.7^2-6.7^2)/дробь 12^2-11.4^2)*(6.4^2-3.6^2)Сократите дробь x^2-x+1/(дробь) x^4+x^2+1 Почему то у меня не получается я не знаю как решить эти примеры заранее спасибо!

Answer 1

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Answer 2

Simplifying the Expression

To simplify the expression (4a/(4-a^2-a-2)/(4+2a))*4/(a+2-a/(2-a), we can follow the order of operations and simplify the terms step by step.

First, let's factorize the denominators and simplify the expression:

1. Factorize the denominators: - The denominator of the first fraction is (4-a^2-a-2), which can be simplified to (2-a)(2+a). - The denominator of the second fraction is (2-a).

2. Simplify the expression: - After factorizing the denominators, the expression becomes: (4a/((2-a)(2+a))/(4+2a))*4/(a+2-a/(2-a)).

3. Now, simplify the expression further: - (4a/((2-a)(2+a))/(4+2a))*4/(a+2-a/(2-a)) can be simplified to (4a/((2-a)(2+a))/(4+2a))*(4/(a+2)).

4. Finally, simplify the expression: - The simplified expression is (4a(4))/((2-a)(2+a)(4+2a)(a+2)).

Example Calculation

Let's calculate the expression (5.2/2-4.8^2)*(16.7^2-6.7^2)/(12^2-11.4^2)*(6.4^2-3.6^2) step by step:

1. Calculate each part of the expression: - 5.2/2-4.8^2 = -2.4 - 16.7^2-6.7^2 = 250 - 12^2-11.4^2 = 23.04 - 6.4^2-3.6^2 = 29.6

2. Substitute the calculated values into the expression: - (-2.4)*(250)/(23.04)*(29.6)

3. Calculate the final result: - The final result is approximately -50.34.

Simplifying a Fraction

To simplify the fraction x^2-x+1/(x^4+x^2+1), we can factorize the denominator and simplify the fraction:

1. Factorize the denominator: - The denominator x^4+x^2+1 can be factorized as (x^2+x+1)(x^2-x+1).

2. Simplify the fraction: - After factorizing the denominator, the fraction becomes x^2-x+1/(x^2+x+1)(x^2-x+1).

3. Finally, simplify the fraction: - The simplified fraction is 1/(x^2+x+1).

I hope this helps! Let me know if you have further questions or need additional assistance.