6-2:Solving Rational Equations Unit 6: Rational and Radical Equations

Recall: Solving basic equations and fraction facts. As long as the denominators are all the same, the numerators are all that matter: 2x + 4 = 12  Just like multiplying all the way through By the common denominator, 11.

Recall: restrictions on domain  Most of the time, the domain was all real numbers, that we wrote as:  We had 2 exceptions: radicals and rationals  Everything under a radical MUST BE greater than zero  You must NEVER have a denominator that equals zero

Example 1: The least common denominator: 9(7) = 63 Multiply each term by 63 Solve the basic equation.

If you have a variable in the denominator, you must be careful to check that the solution is in the domain. There is a variable in the denominator, so y = -2 is not in the domain, which means that we can’t get that for an answer. The common denominator is: 4(7)(y + 2)  28(y + 2) Multiply each term by the LCD to get rid of all fractions. Example 2:

Example 3: Note: Usually, when there are only 2 fractions, you would solve by proportions. Here, the denominators are the same, so like the first slide, you can throw them out. Remember: x ≠ 3

Example 4: What is the domain restriction that we have to pay attention to?

Example 5: What is the domain restriction that we have to pay attention to?