# Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:

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Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:

To solve a rational equation: 1) Find the LCD of all rational expressions in the equation. 2) Multiply both sides of the equation by the LCD. 3) Solve the resulting equation.

Example 1 First determine any restrictions on the variable. These are values of x for which any denominator is zero. Solve: In this case, x cannot be zero.

Determine the LCD Multiply both sides of the equation by the LCD

These solutions must be compared with the restriction on x found at the beginning of the problem, x ≠ 0. Since neither value is zero, we have the solution.

Example 2 Determine any restrictions on the variable. Solve:

Determine the LCD Multiply both sides of the equation by the LCD. This is the same as multiplying every term by the LCD.

Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 4,2. Since the solution does not match either restriction, we have the solution.

Example 3 Determine any restrictions on the variable. Solve:

Determine the LCD Multiply every term by the LCD.

Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 5,0. Since in this case the result is one of the restricted values, it cannot be a solution to the equation. The answer is written as …

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