Solve each equation. 2/x+2 + 1/x+4 = 4/x²+6x+8

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including finding a common denominator and simplifying, is crucial for solving equations involving them. In the given equation, the terms involve rational expressions that need to be combined and simplified to find the solution.

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 provided equation, identifying the least common denominator will help eliminate the fractions and simplify the equation.

Factoring Polynomials

Factoring polynomials is the process of breaking down a polynomial into simpler components, or factors, that can be multiplied together to obtain the original polynomial. This concept is essential when simplifying expressions or solving equations, as it can reveal solutions or make the equation easier to work with. In the context of the given equation, factoring may be necessary to simplify the denominator and solve for x.