Exercises 137–139 will help you prepare for the material covered in the next section. Solve: (x + 2)/(4x + 3) = 1/x

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including simplifying, adding, subtracting, multiplying, and dividing them, is crucial for solving equations involving them. In this problem, both sides of the equation are rational expressions, which requires knowledge of their properties.

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 simplify the equation. This method is particularly useful in this problem to transform the equation into a polynomial equation that can be solved more easily.

Finding Common Denominators

Finding a common denominator is essential when adding or subtracting rational expressions. It allows us to combine fractions into a single expression. In this equation, understanding how to find a common denominator will help in simplifying the equation after cross multiplication, ensuring that all terms can be combined and solved effectively.