x where x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

X where x x x x x x x x x x x x x x x x x x x x x x x

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x where x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
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 4 5 0 4 0 5 0 4 5 0 20 25 3 2 5 2 3 2 2 2 x or x x or x x x x x x x x x MCR3U 0.7.0 Solving Equations with Rational Expressions Ex. 2 Recall clearing fractions by multiplying by the LCD. Unlike simplifying expressions, when solving an equation we have the luxury of being able to multiply (as long as we multiply on both sides). 7 21 3 14 7 3 x x x Recall solving equations by performing opposite operations to both sides to maintain equilibrium. To solve a linear equation, isolate the variable We can determine a common denominator We can clear all fractions by multiplying by a common denominator which equals 6. Ex. 1 Recall , solving a quadratic equation is a little different. Don’t try to isolate the variable. Instead, set the equation to zero, factor, and solve. 23 25 2 2 6 25 2 6 2 6 25 2 6 2 2 3 6 1 2 24 6 1 2 3 6 1 2 4 3 1 2 x x x x x x x x x x x x x x Ex. 3
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MCR3U 0.7.0 Solving Equations with Rational Expressions Solve. Ex. 4 To solve an equation with rational expressions: 1. Factor first 2. Determine the LCD and simplify After factoring, it can be seen that the LCD is: 3. Then clear the denominators by multiplying by the LCD 4. If linear, isolate the variable. If quadratic, set the equation equal to zero, factor, and solve. 5. Check your solution against the restrictions. A solution cannot be a restriction  2 2 x x Solve. Ex. 5     . 7 4 0 7 4 0 28 11 0 84 33 3 75 40 5 9 7 2 15 8 5 10 2 9 3 3 5 5 3 5 3 5 5 2 3 3 5 3 2 5 3 2 2 2 2 2 2 solutions valid are they then ns restrictio not are x or x x x x x x x x x x x x x x x x x x x x x x x x x x x x    solution valid a is x n restrictio a not x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 3 5 3 5 3 5 6 10 2 2 2 2 2 2 , 10 6 0 10 6 2 10 8 2 3 10 5 2 3 2 5 2 2 2 2 2 3 2 5 2 2 2 3 2 5 2 4 3 2 5 Remember, you can divide both sides by -3 3 5 , x or x 2 , x
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MCR3U 0.7.0 Solving Equations with Rational Expressions Solve.     solution valid a is x only then n restrictio a is x x or x x x x x x x x x x x x x x x x x x x x x x x x x 1 , 7 1 7 1 7 0 7 6 0 2 6 5 7 2 5 7 2 1 5 2 7 7 2 1 2 7 5 2 7 1 2 7 5 2 2 2 Ex. 6 2 7 , x or x Do not forget to state restrictions here!
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  • Winter '15
  • Oliver Hyde
  • Fraction, Elementary arithmetic, Greatest common divisor, Least common multiple, Factoring Review

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