6-2:Solving Rational 6-2:Solving Rational EquationsEquations

6-2:Solving Rational 6-2:Solving Rational EquationsEquations

Unit 6: Rational and Radical Unit 6: Rational and Radical EquationsEquations

Recall: Solving basic equations andfraction facts.

2 + 4 = 12

2 = 8

= 4

x

x

x

2 4 12+ =

11 11 11

x As long as the denominators areall the same, the numerators are all that matter: 2x + 4 = 12

Just like multiplying all the way throughBy 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

xxx

Example 1:

+ = 19 7

x x 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 thatthe solution is in the domain.

3 3 9- =

4 + 2 28y

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 3:7 + 4=

- 3 - 3

x

x xNote: Usually, when there are only2 fractions, you would solve byproportions. Here, thedenominators are the same, solike the first slide, you can throwthem out.

Remember: x ≠ 3

4 - 3+ =

-1 -1

w ww

w w

Example 4:

What is the domain restrictionthat we have to pay attention to?

2

+ 3 14 3 - 2- =

- 2 + 2 - 4

x x

x x x

Example 5:

What is the domain restrictionthat we have to pay attention to?