Find the L C D and multiply each term by the L C D . Then solve. Check your solutions. (5 x+7)/(

step 1 The thought process on this one is not just that you're looking for a common denominator, that's

Find the L C D and multiply each term by the L C D . Then...

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Key Concepts

Domain Restrictions and Extraneous Solutions

When dealing with rational equations, it is essential to determine the values that make any original denominator zero and exclude these from the solution set. Even after clearing denominators, some solutions may not be valid in the original equation; these are known as extraneous solutions and must be checked and discarded if necessary.

Solving Rational Equations

This concept involves the techniques required to solve equations that include rational expressions. After clearing denominators with the LCD, the resulting polynomial equation can be solved using standard algebraic methods, and any potential solutions must be verified against the original equation to account for possible restrictions.

Least Common Denominator (LCD)

The LCD is the smallest expression that contains all factors from the denominators of the rational expressions. It allows you to combine fractions or eliminate denominators by multiplying each term by the LCD, thus transforming a rational equation into a polynomial equation.

Clearing the Denominator

Multiplying both sides of a rational equation by the LCD eliminates the fractions, simplifying the equation into a form that is easier to solve. This process must be carefully carried out to ensure that no terms are lost and that the multiplication is valid across the equation.

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