# 10.6 Solving Rational Equations

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10.6 Solving Rational Equations
Goals: To solve problems involving rational expressions

Rational Equation An equation containing one or more rational expressions

Steps to solve Rational Equations
Find the LCD Multiply every term on both sides of the equation by the LCD over 1(objective is to cancel out the denominators) Solve for the variable a. If it is a linear equation get variables on one side and constants on the other b. If it is a quadratric set your equation = 0 and factor.

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) (x + 1)(x)• •(x + 1)(x)

Solve for x: LCM = 2x 2x• •2x

Solve for x: x• • x

Solve for x: -2 is an extraneous solution.

Solve for x: -2 is an extraneous solution.

Cross products Short cut:
extraneous solution?

Cross products:

Cross products:

Cross products:

Assignment: Page 453 # (2-24) even