Question

Сократить дробь x^4+1/x^2+x√2+1; x^2-x+1/x^4+x^2+1

Answer 1

Я не понял! еще раз можно написать

Answer 2

To simplify the given expression, we'll start by finding a common denominator for both fractions. The common denominator will be the product of the denominators of the two fractions. Then we'll combine the fractions and simplify further.

Expression 1: (x^4 + 1) / (x^2 + x√2 + 1) Expression 2: (x^2 - x + 1) / (x^4 + x^2 + 1)

Step 1: Find the common denominator. Common denominator = (x^2 + x√2 + 1) * (x^4 + x^2 + 1)

Step 2: Rewrite the fractions with the common denominator. Expression 1: [(x^4 + 1) * (x^4 + x^2 + 1)] / [(x^2 + x√2 + 1) * (x^4 + x^2 + 1)] Expression 2: [(x^2 - x + 1) * (x^2 + x√2 + 1)] / [(x^4 + x^2 + 1) * (x^2 + x√2 + 1)]

Step 3: Expand the numerators. Expression 1: (x^8 + x^6 + x^4 + x^4 + x^2 + 1) Expression 2: (x^4 + x^3√2 + x^2 - x^3 - x^2√2 - x + x^2 + x√2 + 1)

Step 4: Combine like terms in the numerators. Expression 1: x^8 + x^6 + 2x^4 + x^2 + 1 Expression 2: x^4 + (x^3√2 - x^3) + (x^2 - x^2√2 + x^2) + (x√2 - x) + 1

Step 5: Simplify further. Expression 1: x^8 + x^6 + 2x^4 + x^2 + 1 Expression 2: x^4 + x^3(√2 - 1) + x^2(1 - √2) + x(√2 - 1) + 1

There is no common factor in both expressions, so we cannot simplify them further without knowing specific values for x. Therefore, the simplified expressions are as follows:

Simplified Expression 1: x^8 + x^6 + 2x^4 + x^2 + 1 Simplified Expression 2: x^4 + x^3(√2 - 1) + x^2(1 - √2) + x(√2 - 1) + 1