The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

In algebra, equations can be classified into three main types: identities, conditional equations, and inconsistent equations. An identity holds true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solutions. Understanding these classifications is essential for determining the nature of the given equation.

Rational equations 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. This process is crucial for isolating the variable and finding potential solutions.

After solving an equation, it is important to check the solutions by substituting them back into the original equation. This verification process ensures that the solutions are valid and helps identify any extraneous solutions that may arise, particularly in rational equations where division by zero can occur.