Determine the values of the variable that cannot possibly be solutions of each equation. Do not solve. See Examples 1 and 2. 3/(x-2) + 1/(x+1) = 3/(x^2-x-2)

Key Concepts

Undefined Values

In algebra, certain values of a variable can make an expression undefined, typically when they cause division by zero. For example, in the equation 3/(x-2), if x equals 2, the denominator becomes zero, leading to an undefined expression. Identifying these values is crucial for determining which values cannot be solutions.

Factoring Polynomials

Factoring polynomials involves breaking down a polynomial into simpler components (factors) that, when multiplied together, yield the original polynomial. In the given equation, the expression x^2 - x - 2 can be factored to identify its roots, which are the values that make the equation zero. This process helps in finding restrictions on the variable.

Rational Expressions

Rational expressions are fractions where the numerator and/or denominator are polynomials. Understanding how to manipulate and simplify these expressions is essential for solving equations involving them. In the provided equation, recognizing the rational expressions allows us to determine the values of x that would make the denominators zero, thus identifying the excluded values.