1. Solving Rational Equations Lesson 11.8

2. There are two basic techniques you can choose from to solve rational equations.
Multiply by the least common denominator (LCD)
Cross multiply

3. Least Common Denominator
Find the LCD
Multiply each term by the LCD.
Simplify each term.
Now solve the polynomial using whichever method is easiest.

4. Practice solving rational equations using LCD.
Find the LCD. 3x
Solve: = x x
3x ∙ 2 + 3x ∙ 1 = 3x ∙ x x
Multiply each term by the LCD.
6 + x = 12
Simplify
x = 6

5. Practice solving rational equations using LCD.
Find the LCD. 2x
Solve: x = x 2
2x ∙ 6 + 2x ∙ x = 2x ∙ x
Multiply each term by the LCD.
12 + x2 = 8x
Simplify
x2 – 8x + 12 = 0
(x – 6)(x – 2) = 0
x = 6, 2

6. Cross Multiply Solve: 5 = y y + 2 3 Cross Multiply 15 = y(y + 2)
Simplify
Write in standard form.
Factor
Solve

7. Practice solving rational equations by cross multiplying.
Solve:
3 = x x + 1
Cross Multiply
3(x + 1) = 2(x + 5)
3x + 3 = 2x + 10
x = 7
Simplify
Combine Like-Terms to solve.

8. Which method would be the easiest to use to solve the following problems?
3x = x x - 1 1.
Cross Multiply
2. 4 – x = x
LCD
3. x + 30 = x x
Both ways are equally easy.