Ex 4 Partial Fractions
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Exercise 4: Partial Fractions 1.
Express the following fraction into partial fractions (a)
3 x 10 ( x 2)( x 4)
(g)
x4 (2 x 1)( x 1) 2
(b)
x2 1 x2 1
(h)
4x (3 x 1)( x 1) 2
(i)
4 x 4
(j)
2x 3 (3 x 2)( x 2 1)
(k)
x 1 2x 5x 2 2x
(l)
x2 2 ( x 1)(2 x 1)
(m)
x5 ( x 1) 2 ( x 1)
x 2 5x (c) (1 x)(1 x) 2 (d)
(e)
(f)
4x 9 x ( x 3) 2 x( x 1)( x 1)
x 2 3x 1 ( x 1)( x 2)
2
3
6 7x partial fractions. [4] (2 x)(1 x 2 )
2.
Express in
3.
Express in
4.
Express in
x3 x 2 partial fractions. ( x 1)( x 2 1)
5.
Express in
x 2 7x 6 partial fractions. [4] ( x 1)( x 2)( x 1)
6.
Express in
4x partial fractions. ( x 4)( x 2 3)
9x 2 4 partial fractions. [5] (2 x 1)( x 2) 2 [5]
[5]
Express the following fraction into partial fractions (a)
3 x 10 ( x 2)( x 4)
(g)
x4 (2 x 1)( x 1) 2
(b)
x2 1 x2 1
(h)
4x (3 x 1)( x 1) 2
(i)
4 x 4
(j)
2x 3 (3 x 2)( x 2 1)
(k)
x 1 2x 5x 2 2x
(l)
x2 2 ( x 1)(2 x 1)
(m)
x5 ( x 1) 2 ( x 1)
x 2 5x (c) (1 x)(1 x) 2 (d)
(e)
(f)
4x 9 x ( x 3) 2 x( x 1)( x 1)
x 2 3x 1 ( x 1)( x 2)
2
3
6 7x partial fractions. [4] (2 x)(1 x 2 )
2.
Express in
3.
Express in
4.
Express in
x3 x 2 partial fractions. ( x 1)( x 2 1)
5.
Express in
x 2 7x 6 partial fractions. [4] ( x 1)( x 2)( x 1)
6.
Express in
4x partial fractions. ( x 4)( x 2 3)
9x 2 4 partial fractions. [5] (2 x 1)( x 2) 2 [5]
[5]
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