3. Solving Equations Containing Rational Expressions
§ 6.5
Solving Equations Containing Rational Expressions

4. Solving Equations
First note that an equation contains an equal sign and an expression does not.
To solve EQUATIONS containing rational expressions, clear the fractions by multiplying both sides of the equation by the LCD of all the fractions.
Then solve as in previous sections.
Note: this works for equations only, not simplifying expressions.

5. Solving Equations Example: Solve the following rational equation. true
Check in the original equation.
true

6. Solving Equations Example: Solve the following rational equation.
Continued.

7. Solving Equations Example continued: true So the solution is
Substitute the value for x into the original equation, to check the solution.
true
So the solution is

8. Solving Equations Example: Solve the following rational equation.
Continued.

9. Solving Equations Example continued: true
Substitute the value for x into the original equation, to check the solution.
true
So the solution is

10. Solving Equations Example: Solve the following rational equation.
Continued.

14. Solving Equations Example continued: true So the solution is x = 3.
Substitute the value for x into the original equation, to check the solution.
true
So the solution is x = 3.

15. Solving Equations Example: Solve the following rational equation.
Continued.

16. Solving Equations Example continued:
Substitute the value for x into the original equation, to check the solution.
Since substituting the suggested value of a into the equation produced undefined expressions, the solution is .