Solve each equation. 2 - 5/x = 3/x²

Key Concepts

Rational Equations

Rational equations are equations that involve fractions with polynomials in the numerator and denominator. To solve these equations, one typically finds a common denominator to eliminate the fractions, allowing for easier manipulation and simplification. Understanding how to work with rational expressions is crucial for solving equations like the one presented.

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, and vice versa, one can eliminate the fractions and simplify the equation. This method is particularly useful in rational equations, making it easier to isolate variables.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax² + bx + c = 0, where a, b, and c are constants. They can be solved using various methods, including factoring, completing the square, or the quadratic formula. In the context of the given equation, recognizing that the manipulation leads to a quadratic form is essential for finding the solutions.