7'6 Solving Rational Equations and Formulas

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7.6 Solving Rational Equations and Formulas
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Rational Equation

• A rational or fractional equation is an equation
  containing one or more rational expression.
• Examples of a rational equation

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Solving Rational Equations

• List restrictions on the variable. Avoid any
  values of the variable that make a denominator
  equal zero.
• Clear the equation of fractions by multiplying
  both sides by the LCD of all rational expressions
  in the equation.
• Solve the resulting equation.
• Reject any proposed solution that is in the list
  of restrictions on the variable. Check other
  proposed solutions in the original equation.

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Solve

There are no restrictions on x.
Multiply both sides by the LCD, 30.
Use the distributive property. Simplify.
10x 25 6x
x 25/4
Isolate x.
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Solve continued.

Check the solution x 25/4 in the original
equation. By hand or on the calculator.
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Solve

By factoring each denominator we observe that the
restrictions are x ? 5, x ? -5. Also, we see that
the LCD is (x5)(x-5).
Multiply both sides by the LCD, (x5)(x-5).
Use the distributive property to eliminate the
denominators.
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Solve continued.
Simplify. The equation is cleared of fractions.

Use the distributive property.
Combine like terms on the left side.
Add x to both sides.
Solve for x, divide both sides by 5.
The solution is x - 3. (Note that It checks in
the original equation and is not part of the
restriction.)
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7.6 Solving Rational Equations and Formulas
Def A formula is an equation that gives a
relationship between two or more variables.
Formulas are used in all sorts of areas.
Examples 1) E mc2 2) Sa/(1-r) 3) 1/p 1/q
1/f
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7.6 Solving Rational Equations and Formulas
Solve for m
Multiply both sides by the LCD (Rm)
Distribute I
Isolate the term with m
Divide both sides by I
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7.6 Solving Rational Equations and Formulas
The notes have been created using the book by
Blitzer, Introductory and Intermediate Algebra