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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