Solving Rational EquationsLesson 4

ObjectivesFind the values that will make a rational expression undefined(excluded values)

Solve rational equations

Algebraic Fraction/Rational Expression

Since a RE indicates division, we cannot replace the variables in a denominator with numbers that make the denominator zero.

State the value of the variable that will make the expression

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State the value of the variable that will make the expression

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State the value of the variable that will make the expression

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State the value of the variable that will make the expression

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Recall: Find the LCD

Recall: Find the LCD

Recall: Find the LCD

Solving Rational Equations

1. Identify and exclude any values that will make the denominator zero.

2. Multiply both sides by the LCD and simplify (this will eliminate all denominators).

3. Solve the resulting equation.4. Check all solutions in the original

equation.

Example 12Solve the equation.

Multiply by the LCD: 15

Example 13Solve the equation.

Example 13

Check:We need 2b – 5 ≠ 0 and b – 3 ≠ 0which means b ≠ 5/2 and b ≠ 3.

multiply by LCD.

Simplify – denominators are eliminated

Distribute

Solve for b.

Solve for m.

Since m2- m = m(m – 1), the LCD is m(m – 1), where m≠0 and m ≠ 1.

Solve for m.

2(m – 1) – m = 4 2m - 2 - m = 4 m = 6

Simplify – denominators are eliminated

Distribute

Solve for m.

multiply by LCD.

Solve for x.

x2 – 3x + 12 = x – 3 + 4xx2 – 8x + 15 = 0(x – 3)(x – 5) = 0x = 3 or x = 5

Simplify – denominators are eliminatedSet equation equal to zero.

Factor.Zero factor property

multiply by LCD.

x = 3 is an extraneous root and x =5 is the only solution.

SOLVING RATIONAL EQUATIONS• Find the LCD• Multiply both sides of the equation

by the LCD.• Solve using APE/MPE and/or• Solve by factoring.• Cross check solutions with

restrictions

Solve for x.

Solve for y.