Lecture 8 - Equations involving Rational Expressions Radicals Absolute Values and those in Quadratic Form Mathematics 17 Institute of Mathematics

Lecture 8 - Equations involving Rational Expressions...

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Equations involving Rational Expressions, Radicals, Absolute Values, and those in Quadratic Form Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 8 Math 17 (UP-IMath) Equations Lec 8 1 / 19
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Outline 1 Rational Equations in x 2 Equations involving Radicals 3 Equations in Quadratic Form 4 Equations Involving Absolute Values 5 Solving Equations via Factoring Math 17 (UP-IMath) Equations Lec 8 2 / 19
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Equations involving Rational Expressions To solve: Math 17 (UP-IMath) Equations Lec 8 3 / 19
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Equations involving Rational Expressions To solve: 1 Multiply the LCD to both sides of the equation 2 Solve the equation that arises 3 Drop any of the obtained solutions that make the rational expressions undefined (extraneous solutions). Math 17 (UP-IMath) Equations Lec 8 3 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 x 2 - x - 20 = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 x 2 - x - 20 - (2 x 2 + x - 6) = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 x 2 - x - 20 - (2 x 2 + x - 6) = 3 x - 8 x 2 - x - 20 - 2 x 2 - x + 6 = 3 x - 8 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 . Solution: ( x - 5)( x + 2) h x +4 x +2 - 2 x - 3 x - 5 i = 3 x - 8 x 2 - 3 x - 10 · ( x - 5)( x + 2) ( x - 5)( x + 4) - (2 x - 3)( x + 2) = 3 x - 8 x 2 - x - 20 - (2 x 2 + x - 6) = 3 x - 8 x 2 - x - 20 - 2 x 2 - x + 6 = 3 x - 8 - x 2 - 5 x - 6 = 0 Math 17 (UP-IMath) Equations Lec 8 4 / 19
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Example: Solve x +4 x +2 - 2 x - 3 x - 5 = 3 x - 8 x 2 - 3 x - 10 .
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