Lesson #13 Adding & Subtracting Rational Expressions

Recall that to add fractions together you first need to have everything over a common denominator.

STEPS: Adding and Subtracting rats

Step 1: Factor and reduce each fractionStep 2: Find a common denominator and change numeratorsStep 3: Perform the operationsStep 4: Factor again and reduce if possibleStep 5: State restrictions

€

+ 12(x −1)

(x − 3)(x −1)

€

x + 3

(x − 3)(x + 3)

Ex. 1 Simplify and state restrictions

€

1. 2

x −1

€

+ 3

x −1

€

=2 + 3

x −1

€

= 5

x −1

€

x ≠1

€

2. x + 3

x 2 − 9

€

+ 12x − 24

x 2 − 4x + 3

€

=

€

=1

x − 3

€

+ 12

x − 3

€

= 13

x − 3

€

x ≠ {−3, 1, 3}

€

3. 5a+ 5b

a2 + 2ab+b2

€

+ 8a

−a −b

€

=5(a+b)

(a+b)(a+b)

€

−8a

a+b

€

=5

a+b

€

− 8a

a+b

€

= 5 − 8a

a+b

€

a ≠ −b

€

4. 7a

bc−

6

a

€

=7a2

abc

€

−6bc

abc

€

=7a2 − 6bc

abc

€

a ≠ 0, b ≠ −, c ≠ 0

Use the propertyEx. 2 a

c +

d = a d + c

c d

€

1. 10

x

€

+ 3

y

€

= 10y

€

+ 3x

€

xy

€

x ≠ 0, y ≠ 0€

2. 4

x −1+

1

x +1

€

(x −1)(x +1)

€

= 4(x +1)

€

+ 1(x −1)

€

(x −1)(x +1)

€

= 4x + 4 + x −1

€

= 5x + 3

(x −1)(x +1)

€

x ≠ ±1

€

1. 7x 2 −14x

x 2 − 9x +14−

49

x − 7

€

=7x(x − 2)

€

(x − 7)(x − 2)

€

−49

x − 7

€

=7x

x − 7

€

−49

x − 7

€

=7x − 49

x − 7

€

=7(x − 7)

x − 7

€

=7

Subtract these rational expressionsEx. 3

€

x ≠ 2,7

€

2. 4x

x 2 −1−

3

x −1

€

=4x

(x −1)(x +1)−

3

x −1

€

=4x − 3(x +1)

(x −1)(x +1)

€

=4x − 3x − 3

(x −1)(x +1)

€

=x − 3

(x −1)(x +1)

€

x ≠ ±1

€

3. 2x

x + 4−

x

3x −1

€

=2x(3x −1)

€

−x(x + 4)

€

(x + 4)(3x −1)

€

=6x 2 − 2x − x 2 − 4x

€

=5x 2 − 6x

(x + 4)(3x −1)

€

x ≠ {−4,−1

3}

€

(x + 4)(3x −1)

€

= x(5x − 6)

(x + 4)(3x −1)

Homework

Pg. 28 #5-8 in the WorkbookSolutions posted on mrharvey.ca