Express the rational function as a sum or difference of two simpler rational expressions. 2x (x+2)² 4 + x+2 (x+2)² 3 x+2 (r+2)² 4 x+2 (x+2)² 4 x+2 (x+2)²
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![### Express the Rational Function as a Sum or Difference of Two Simpler Rational Expressions
Given the rational function:
\[ \frac{2x}{(x+2)^2} \]
We need to express this function as a sum or difference of two simpler rational expressions. The options provided are:
1. \[ \frac{2}{x+2} + \frac{4}{(x+2)^2} \]
2. \[ \frac{2}{x+2} - \frac{3}{(x+2)^2} \]
3. \[ \frac{1}{x+2} - \frac{4}{(x+2)^2} \]
4. \[ \frac{2}{x+2} - \frac{4}{(x+2)^2} \]
### Explanation
The goal is to decompose the given rational function into a form that simplifies the understanding and manipulation of the expression. Each option represents a possible way to break down the given rational function.
- The numerator and the denominator in each option suggest different ways to express \( \frac{2x}{(x+2)^2} \) by separating the terms into simpler fractions with \( (x+2) \) and \( (x+2)^2 \) denominators.
- The first option involves adding two fractions with the denominators \( x+2 \) and \( (x+2)^2 \).
- The second, third, and fourth options involve subtracting two fractions where both include \( x+2 \) or \( (x+2)^2 \) in the denominators.
To solve this, you would need to verify which of these decompositions results in the original function \( \frac{2x}{(x+2)^2} \) when combined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30c07f2b-13db-4887-9bcb-8633a00a882e%2F666dee3d-a014-4ec6-8309-da7c80a3db98%2Ftinu8r_processed.png&w=3840&q=75)
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