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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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.
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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.
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Determine the LCD Multiply both sides of the equation by the
LCD
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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.
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Example 2 Determine any restrictions on the variable.
Solve:
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Determine the LCD Multiply both sides of the equation by the
LCD. This is the same as multiplying every term by the LCD.
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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.
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Example 3 Determine any restrictions on the variable.
Solve:
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Determine the LCD Multiply every term by the LCD.
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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
