Solving Rational Equations

Lesson 11.8

There are two basic techniques you can choose

from to solve rational equations.

1. Multiply by the least common denominator (LCD)

2. Cross multiply

Least Common Denominator

1. Find the LCD

2. Multiply each term by the LCD.

3. Simplify each term.

4. Now solve the polynomial using whichever method is easiest.

Practice solving rational equations using LCD.

Solve: 2 + 1 = 4 x 3 x

Find the LCD.

3x

3x ∙ 2 + 3x ∙ 1 = 3x ∙ 4 x 3 x

Multiply each term by the LCD.

6 + x = 12 Simplify

x = 6

Practice solving rational equations using LCD.

Solve: 6 + x = 4 x 2

Find the LCD.

2x

2x ∙ 6 + 2x ∙ x = 2x ∙ 4 x 2

Multiply each term by the LCD.

12 + x2 = 8x

Simplifyx2 – 8x + 12 = 0

(x – 6)(x – 2) = 0

x = 6, 2

Cross Multiply

5 = yy + 2 3

Solve:

Cross Multiply

15 = y(y + 2)

15 = y2 + 2y

0 = y2 + 2y – 15

0 = (y + 5)(y – 3)

y = -5, 3

Simplify

Write in standard form.

FactorSolve

Practice solving rational equations by cross

multiplying.

3 = 2 .x + 5 x + 1

Solve:

Cross Multiply

3(x + 1) = 2(x + 5)

3x + 3 = 2x + 10

x = 7

Simplify

Combine Like-Terms to solve.

Which method would be the easiest to use to solve the

following problems? 3x = 2 .x + 1 x - 1

1. Cross Multiply

2. 4 – x = 5 x 6 3 LCD

3. x + 30 = x x Both ways are equally

easy.