SAT Prep: Solving Rational Equations Goals: To solve problems involving rational expressions (equations that have variables in the denominator)

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Presentation transcript:

SAT Prep: Solving Rational Equations Goals: To solve problems involving rational expressions (equations that have variables in the denominator)

Steps to solve SAT Rational Equations If you see one fraction equal another fraction (which is a popular SAT format for rational equations) all you have to do is CROSS – MULTIPLY!! But remember, you will often be asked to do something with your value that you solve for! For example, if 5x + 7 = -3, what does 6x equal?

Extraneous Solutions When both sides of the equation are mult by a variable, the equation is transformed into a new equation and may have an extra solution. Check each solution in the original rational equation Make sure that your answer does not make the denominator 0

Solving Rational Equations Multiply both sides of the equation by the LCM of the denominators. Least Common Multiple: Each factor raised to the greatest exponent.

Solve for x: LCM =

Solve for x: LCM = (x + 1)(x)

Solve for x: LCM = 2x

Cross products Short cut: extraneous solution?

Solve for x: x x

-2 is an extraneous solution.

Solve for x: -2 is an extraneous solution.

Cross products:

Assignment: Page 453 # (2-24) even