Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational...

Adding & Subtracting Rational Expressions

9/27/2015 7:22 PM4.3: Add and Subtract Rational Expressions

1

Example 1

Simplify 5𝑥

2𝑦+

𝑥

2𝑦

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 2

3x

y

6

2

x

y

3

Example 2

Simplify 3𝑥2+2𝑥

𝑥−1−

10𝑥−5

𝑥−1

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 3

3 5x

23 2 10 5

1

x x x

x

23 2 10 5

1

x x x

x

23 8 5

1

x x

x

3 5 1

1

x x

x

Your Turn

Simplify 2𝑥2+5𝑥

𝑥+2−

4𝑥+6

𝑥+2

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 4

2 3x

22 5 4 6

2

x x x

x

22 5 4 6

2

x x x

x

22 6

2

x x

x

2 3 2

2

x x

x

Steps of Add & Subtract Rational Expressions

A. When given an equation, rewrite the fraction using the common denominator.

B. Simplify by combining like terms of both the numerator and denominator.

C. Multiply if needed and then simplify.

D. Reduce to lowest terms up top. Do NOT distribute the bottom.

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 5

Review

• What is the common denominator of 6 and 15?

• What is the common denominator of 3x and 9x2?

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 6

30

29x

Example 3

Find the LCD of (x + 2) and (x – 2)

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 7

2 2x x

1 1

2 2x x

Example 4

Find the LCD

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 8

2 2

1 1

6 3 2t t t t

3 2 1t t t

1

2 3t t 1

1 2t t

1

2 31t t t

3

1

1 2t tt

Your Turn

Find the LCD of (x – 4)2 and (3x – 12)

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 9

2

3 4x

Example 5

Simplify

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 10

13

24x

7 5

6 8x x 3 4

4 3

24 24x x

28 15

Example 6

Simplify 3

𝑥−3+

5

𝑥+2What is the common denominator?

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 11

3 2x x

3 5

3 2 3 2x x x x

2x 3x

Example 6

Distribute the top.

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 12

3 2 5 3

3 2 3 2

x x

x x x x

3 6 5 15

3 2 3 2

x x

x x x x

Example 6

Simplify 3

𝑥−3+

5

𝑥+2

Combine like terms.

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 13

3 6 5 15

3 2 3 2

x x

x x x x

8 9

3 2

x

x x

Example 7Simplify

10𝑥

𝑥2−9−

5

𝑥+3

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 14

5

3x

10 5

3 3 3

x

x x x

10 5

3 3 3 3

x

x x x x

(x-3)

10 5 15

3 3

x x

x x

5 15

3 3

x

x x

5 3

3 3

x

x x

Example 8

• Simplify

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 15

2

5 2 3

3 2x x x

2 2 26 6 6x x x

(6)

10x

(3x)

2

10 12 9

6

x x

x

2

19 12

6

x

x

(2x)

9x12

Your Turn

Simplify 3

𝑥+2−

8

𝑥−2

9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 16

5 22

2 2

x

x x

3 8

2 2 2 2x x x x

(x-2) (x+2)

3 6 8 2

2 2

x x

x x

3 6 8 16

2 2

x x

x x