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Title: Algebra _ Partial fractions
Description: Algebra _ Partial fractions What are Partial Fractions? When a rational expression is split into the sum of two or more rational expressions, the rational expressions that are a part of the sum are called partial fractions. This is referred to as splitting the given algebraic fraction into partial fractions.
Description: Algebra _ Partial fractions What are Partial Fractions? When a rational expression is split into the sum of two or more rational expressions, the rational expressions that are a part of the sum are called partial fractions. This is referred to as splitting the given algebraic fraction into partial fractions.
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Algebra
Partial fractions
1
...
x
x2 – 1
1
2(x + 4)
2
1
2
1
1 = B(2) B=
2
Put x = 1
1 = A (2) A =
Put x = 1
The partial fractions are
x
(x + 1)( x + 2)
Solution:
1
2
x
x
A
B
=
=
+
x –1
(x +1)(x –1)
x +1
x –1
Solution:
3
...
x+1
x( x - 1)
Solution:
x+1
x( x 1)
=
x+1
A
x
B
+ x–1
= A (x – 1) + Bx
= A ( 1) A = 1
put x = 0
1
put x = 1
2 = B (1)
B=2
The partial fraction are = 1
x
2x 3
5
(
x
+ 2)( x + 3)
2x 3
Solution:
=
(x + 2)( x + 3)
2x 3 =
2
x–2
A
B
+
x+2
x+3
A( x + 3) + B(x +2)
put x = 2,
7 =
A(1) A = 7
put x = 3,
9 =
B(1) B = –9
The partial fraction are = 7
9
x+ 2
x +3
6
...
x2
(2x+1) (2x – 1)
Solution:
Let
¼
1
1
0 –1
4
1
2
1
put x = 2
put x =
=
A(2x – 1) + B(2x + 1)
1
1
4 A (2) A =
8
1
1
= B (2) B = 8
8
1
4
The partial fractions are
8
...
x 1
Solution:
=
B
C
+
x+3
x+4
(3x+2) (x +3)( x+4)
x –1 = A(x +3) (x + 4)+ B(3x +2) (x + 4) + C (3x +2) ( x + 3)
2
Put x =
3
Put x = 3
5
2
2
3
3
3
3
7
5
3
3
Put x = 4
10
3
4 = B (7) (1)
5
The partial fractions are
10
...
x2+ x + 1
(x 2)2 (x +2)
x2+ x + 1
(x 2)2 (x +2)
Solution: Let
Put x = 2,
+
x+ 2
B
x2
+
C
(x– 2)2
3x2 – 1
= A(x – 2) + B(x – 2) + C
12 – 1
= C C = 11
Coefficient of x2
Put x = 0,
=
3
= A
1
= 4A – 2B + C
1
= 12 – 2B + 11
–2B = 24
B = 12
The partial fractions are
12
Title: Algebra _ Partial fractions
Description: Algebra _ Partial fractions What are Partial Fractions? When a rational expression is split into the sum of two or more rational expressions, the rational expressions that are a part of the sum are called partial fractions. This is referred to as splitting the given algebraic fraction into partial fractions.
Description: Algebra _ Partial fractions What are Partial Fractions? When a rational expression is split into the sum of two or more rational expressions, the rational expressions that are a part of the sum are called partial fractions. This is referred to as splitting the given algebraic fraction into partial fractions.