8.5 – Add and Subtract Rational Expressions. When you add or subtract fractions, you must have a...
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Transcript of 8.5 – Add and Subtract Rational Expressions. When you add or subtract fractions, you must have a...
8.5 – Add and Subtract Rational Expressions
When you add or subtract fractions, you must have a common denominator.
a b a b
c c c
a b a b
c c c
When you subtract, make sure to distribute the negative!
1. Perform the indicated operation and simplify.
a. 7 5
12 12x x =
2
12x6
1
6x=
1
1. Perform the indicated operation and simplify.
b. 2
2 2
6 5
3 10 3 10
x x
x x x x
=
2
2
6 5
3 10
x x
x x
5 1
5 2
x x
x x
1
2
x
x
=
1. Perform the indicated operation and simplify.
c.
2
2 2
2 2 4
1 1
x x
x x
=
2
2
2 2 4
1
x x
x
2
2
2( 2)
1
x x
x
2( 1)( 2)
1 1
x x
x x
2 2
1
x
x
=
What if you have unlike denominators?
Find the least common denominator!
2. Find the least common multiple.
35x and 210 15x x5x(2x – 3)
5x3(2x – 3)
a.
2. Find the least common multiple.
24 16x and 26 24 24x x 4(x2 – 4) 6(x2 – 4x + 4)
6(x – 2)24(x – 2)(x + 2)
12(x – 2)2(x + 2)
b.
3. Perform the indicated operation.
3 1
4 6x 9 2
12 12
x
x x =
2x32x3 9 2
12
x
x
2 9
12
x
x
4. Perform the indicated operation.
4 2
4 6x x
x + 4
x + 4
x + 6
x + 6 =
4 6 2 4
4 6
x x
x x
4 24 2 8
4 6
x x
x x
6 32
4 6
x
x x
2 3 16
4 6
x
x x
5. Perform the indicated operation.
2
2 2 1
2 2 4 3
x x
x x x
=
2x – 3
2x – 3
2 6 4 2
2 1 3
x x x
x x
4
2 3
x
x
2 2 1
2( 1) 3 1
x x
x x x
2 3 2 2 1
2 1 3
x x x
x x
2 3 4
2 1 3
x x
x x
1 4
2 1 3
x x
x x
6. Perform the indicated operation.
2
3 1 3
5 325
x x
x xx
=
3 2 3
( 5)( 5) 5 3
x
x x x x
3 3 2 3 5 3 5 5
3 ( 5)( 5)
x x x x x x
x x x
(x+3)(x+3)(x+5) (x-5)(x+5)
2 2 26 9 2 8 15 3 25
3 ( 5)( 5)
x x x x x
x x x
2 2 26 9 2 16 30 3 75
3 ( 5)( 5)
x x x x x
x x x
2 2 26 9 2 16 30 3 75
3 ( 5)( 5)
x x x x x
x x x
6. Perform the indicated operation.
22 10 96
3 ( 5)( 5)
x x
x x x
22 5 48
3 ( 5)( 5)
x x
x x x
Complex Fraction:
Fraction in the numerator or denominator
How To solve:
Multiply the numerator and denominator by the least common multiple of every fraction in the numerator and denominator
7. Simplify.
6 37
5 10
x x
x
6060 10 20
12 42
x x
x
= =
10
2(6 21)
x
x
=
5
6 21
x
x
-5
8. Simplify.
35
2 13 5
x
x x
(x+5)(x-3)(x+5)(x-3)
=
3 3
2 5 3
x
x x
3 3
2 10 3
x
x x
3 3
3 7
x
x