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Solving Rational Equations Lesson 11.8

Learn to solve rational equations using two fundamental techniques: Multiply by the Least Common Denominator (LCD) and Cross Multiply. Practice examples provided to enhance your skills!

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Solving Rational Equations Lesson 11.8

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  1. Solving Rational EquationsLesson 11.8

  2. There are two basic techniques you can choose from to solve rational equations. • Multiply by the least common denominator (LCD) • Cross multiply

  3. Least Common Denominator • Find the LCD • Multiply each term by the LCD. • Simplify each term. • Now solve the polynomial using whichever method is easiest.

  4. Practice solving rational equations using LCD. Find the LCD. 3x Solve: 2 + 1 = 4 x 3 x 3x∙ 2 + 3x ∙ 1 = 3x ∙ 4 x 3 x Multiply each term by the LCD. 6 + x = 12 Simplify x = 6

  5. Practice solving rational equations using LCD. Find the LCD. 2x Solve: 6 + x = 4 x 2 2x∙ 6 + 2x ∙ x = 2x ∙ 4 x 2 Multiply each term by the LCD. 12 + x2 = 8x Simplify x2 – 8x + 12 = 0 (x – 6)(x – 2) = 0 x = 6, 2

  6. Cross Multiply Solve: 5 = yy + 2 3 Cross Multiply 15 = y(y + 2) 15 = y2 + 2y 0 = y2 + 2y – 15 0 = (y + 5)(y – 3) y = -5, 3 Simplify Write in standard form. Factor Solve

  7. Practice solving rational equations by cross multiplying. Solve: 3 = 2 .x + 5 x + 1 Cross Multiply 3(x + 1) = 2(x + 5) 3x + 3 = 2x + 10 x = 7 Simplify Combine Like-Terms to solve.

  8. Which method would be the easiest to use to solve the following problems? 3x = 2 .x + 1 x - 1 1. Cross Multiply 2. 4 – x = 5 x 6 3 LCD 3. x + 30 = x x Both ways are equally easy.

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