Question

2x^2+4x/x^3-8 * x-2/x+2 Тема: умножение и деление рациональных дробей Заранее спасибо

Answer 1

2x² + 4x = 2x( x + 2 ) 
x³ - 8 = ( x - 2 )( x² + 2x + 4 ) 
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( 2x( x + 2 ))/( ( x - 2 )( x² + 2x + 4 )) * ( ( x - 2 )/( x + 2 )) = 2x / ( x² + 2x + 4 )

Answer 2

Rational Expressions Multiplication and Division

When dealing with rational expressions, it's important to simplify the expressions by factoring and canceling out common factors. Let's address the given expression: 2x^2 + 4x / x^3 - 8 * x - 2 / x + 2.

To simplify this expression, we can follow these steps:

1. Factor the denominators and numerators. 2. Cancel out common factors. 3. Perform the multiplication and division.

Let's break down the steps to simplify the given rational expression.

Step 1: Factor the Denominators and Numerators

The given expression is: 2x^2 + 4x / x^3 - 8 * x - 2 / x + 2

The denominator x^3 - 8 can be factored using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, x^3 - 8 can be factored as (x - 2)(x^2 + 2x + 4) [[6 #]].

Step 2: Cancel Out Common Factors

After factoring, we can cancel out common factors in the expression.

Step 3: Perform the Multiplication and Division

Now, we can perform the multiplication and division of the rational expressions.

The simplified expression will be: 2(x + 2) / (x - 2)(x^2 + 2x + 4)

This is the simplified form of the given rational expression.

If you have any further questions or need additional assistance, feel free to ask!