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A complete list of steps for solving a rational equation is outlined in the following example. Example \(\PageIndex{3}\): Solve: \(\dfrac { 2 x } { 3 x + 1 } = \dfrac { 1 } { x - 5 } - \dfrac { 4 ( x - 1 ) } { 3 x ^ { 2 } - 14 x - 5 }\).
Learn the best ways to solve rational equations by eliminating the denominators using the least common denominator (LCD) method. This usually simplifies the problem into solving either a linear or quadratic equation.
Solve rational equations by clearing the fractions by multiplying both sides of the equation by the least common denominator (LCD). Example 7.5.1 7.5. 1. Solve: 5 x − 13 = 1 x 5 x − 1 3 = 1 x. Solution: We first make a note that x ≠ 0 x ≠ 0 and then multiply both sides by the LCD, 3x 3 x:
A rational equation is an equation that contains fractions with xs in the numerator, denominator or both. Here is an example of a rational equation: (4 / (x + 1)) - (3 / (x - 1)) =...
Solve rational equations resulting from setting functions equal to each other. Solve rational equations with extraneous solutions. Equations that contain rational expressions with a variable in at least one denominator are called rational equations. For example, 4 2x + 1 = 2x 3 is a rational equation. Rational equations can be useful for ...
Solve a Rational Equation for a Specific Variable. When we solved linear equations, we learned how to solve a formula for a specific variable. Many formulas used in business, science, economics, and other fields use rational equations to model the relation between two or more variables.
Solve rational equations; Use rational functions; Solve a rational equation for a specific variable