Solving Rational Equations Lesson 11.8

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Presentation transcript:

Solving Rational Equations Lesson 11.8

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

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

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

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

Cross Multiply Solve: 5 = y y + 2 3 Cross Multiply 15 = y(y + 2) Simplify Write in standard form. Factor Solve

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.

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.