Fracciones parciales

1
Gu´ ıa 8 Fracciones Parciales 1. Exprese en fracciones parciales las siguientes funciones racionales. a ) F (x)= 4 x 2 +2x +1 b ) F (x)= 2x x 2 - 1 c ) F (x)= 2x 2 - 1 2x 3 +3x 2 - 2x d ) F (x)= 1 x 3 - 8 e ) F (x)= 6x - 1 (x + 1)(x + 3)(x - 2) f ) F (x)= x 4 - 2x 2 +4x +1 x 3 - x 2 - x +1 g ) F (x)= x (2x + 6)(x 2 + 1)(x 2 + 4) h ) F (x)= x +4 x 3 + x i ) F (x)= x 2 + x +2 (x 2 +2x)(x + 2) j ) F (x)= x 2 +9x +2 (x - 1) 2 (x + 3) k ) F (x)= 30 x 3 - x 2 - x +1 l ) F (x)= 2x 2 + 10x (x 2 - 2x + 5)(x - 1) m ) F (x)= x 3 + x 2 +1 x(x - 1)(x 2 + x + 1) n ) F (x)= 2x + 10 (x + 2)(x 2 + 1) 2 2. Separar las siguientes expresiones racionales, utilizando fracciones parciales. a ) F (x)= x 2 +4 x 2 +2x +1 b ) F (x)= x 3 +5 x 3 - 4x c ) F (x)= 3x 3 +5x +4 (x 2 + 1)(x + 2) d ) F (x)= 4x 4 +3 x 3 +2x 2 - 3x e ) F (x)= x 4 +3x +2 x 4 - 1 f ) F (x)= x 4 +4x +5 (x + 2) 3 g ) F (x)= x 4 - 2x 2 +4x +1 x 3 - x 2 - x +1 h ) F (x)= 2x 5 + 12 x 3 +2x 2 - 2x - 1 1

description

dgfaregaergargaergaerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrg

Transcript of Fracciones parciales

  • Gua 8Fracciones Parciales

    1. Exprese en fracciones parciales las siguientes funciones racionales.

    a) F (x) =4

    x2 + 2x+ 1

    b) F (x) =2x

    x2 1

    c) F (x) =2x2 1

    2x3 + 3x2 2xd) F (x) =

    1

    x3 8e) F (x) =

    6x 1(x+ 1)(x+ 3)(x 2)

    f ) F (x) =x4 2x2 + 4x+ 1x3 x2 x+ 1

    g) F (x) =x

    (2x+ 6)(x2 + 1)(x2 + 4)

    h) F (x) =x+ 4

    x3 + x

    i) F (x) =x2 + x+ 2

    (x2 + 2x)(x+ 2)

    j ) F (x) =x2 + 9x+ 2

    (x 1)2(x+ 3)k) F (x) =

    30

    x3 x2 x+ 1l) F (x) =

    2x2 + 10x

    (x2 2x+ 5)(x 1)

    m) F (x) =x3 + x2 + 1

    x(x 1)(x2 + x+ 1)n) F (x) =

    2x+ 10

    (x+ 2)(x2 + 1)2

    2. Separar las siguientes expresiones racionales, utilizando fracciones parciales.

    a) F (x) =x2 + 4

    x2 + 2x+ 1

    b) F (x) =x3 + 5

    x3 4xc) F (x) =

    3x3 + 5x+ 4

    (x2 + 1)(x+ 2)

    d) F (x) =4x4 + 3

    x3 + 2x2 3x

    e) F (x) =x4 + 3x+ 2

    x4 1f ) F (x) =

    x4 + 4x+ 5

    (x+ 2)3

    g) F (x) =x4 2x2 + 4x+ 1x3 x2 x+ 1

    h) F (x) =2x5 + 12

    x3 + 2x2 2x 1

    1