Solve each equation. x/x+2 + 1/x+3 = 2/x²+2x

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including finding a common denominator and simplifying, is crucial for solving equations involving them. In this question, the rational expressions must be combined and simplified to isolate the variable.

Finding a Common Denominator

To solve equations involving rational expressions, it is often necessary to find a common denominator. This allows for the combination of fractions into a single expression, making it easier to solve for the variable. In the given equation, identifying the least common denominator will help eliminate the fractions and simplify the solving process.

Cross-Multiplication

Cross-multiplication is a technique used to solve equations involving two fractions set equal to each other. By multiplying the numerator of one fraction by the denominator of the other, we can eliminate the fractions and create a polynomial equation. This method is particularly useful in this problem to simplify the equation and isolate the variable.