Efficient Techniques for Solving Rational Equations

Dec 12, 2025

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This guide provides a step-by-step approach to solving rational equations quickly and effectively. A key method is to multiply all terms by the least common denominator (LCD) to eliminate fractions. However, be cautious of potential extraneous solutions. Examples are included to illustrate the process, such as using the LCD to simplify and solve equations, and employing cross-multiplication when fractions are present on both sides of the equation. Don’t forget to check your solutions for accuracy!

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Efficient Techniques for Solving Rational Equations

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2.7 Solving Rational Equations p.228
Hint for solving: • A quick way to solve a rational equation is to multiply everything through by the LCD. • This will get rid of all the fractions! • Beware of extraneous solutions!
Example: Solve. LCD: 2x Multiply each fraction through by the LCD Check your solution!
Solve. LCD: ? LCD: (x+1) ? Check your solution! No Solution!
Solve. Factor 1st! LCD: (x+2)(x-2) Check your solutions!
Short Cut! When there is only fraction on each side of the =, just cross multiply as if you are solving a proportion.
Example: Solve. Check your solutions!
Last Example: Solve. Check your solutions!
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