Ejercicios Matematicos

1.

(8x+1)/(x-2)(x-3) =A/((x-2) )+B/((x+3) ); 8x+1=A(x+3)+B(x-2);

x=2; 17=A(5); A=17/5

x=-3; -23=B(-5); B=23/5

(8x+1)/(x-2)(x-3) =(17/5)/((x-2) )+(23/5)/((x+3) );

2.

(x+29)/(x-4)(x+1) =A/((x-4) )+B/((x+1) ); x+29=A(x+1)+B(x-4);

x=4; 33=A(5); A=33/5

x=-1; 28=B(-5); B=(-28)/5

(x+29)/(x-4)(x+1) =(33/5)/((x-4) )-(28/5)/((x+1) )

3.

(x-24)/(x^2-4x-12)=(x-24)/((x-6)(x+2))=A/((x-6) )+B/((x+2) ); x-24=A(x+2)+B(x-6);

x=6; -18=A(8); A=(-18)/8=-9/4

x=-2; -26=B(-8); B=26/8=13/4

(x-24)/(x^2-4x-12)=(-9/4)/((x-6) )+(13/4)/((x+2) )

4.

(5x+12)/(x^2-4x)=(5x+12)/(x(x-4))=A/x+B/((x-4) ); 5x+12=A(x-4)+B(x);

x=0; 12=A(-4); A=(-12)/4=-3

x=4; 32=B(4); B=32/4=8

(5x+12)/(x^2-4x)=(-3)/x+8/((x-4) )

5.

(〖4x〗^2-15x-1)/(x-1)(x+2)(x-3) ==A/((x-1) )+B/((x+2) )+C/((x-3) );

〖4x〗^2-15x-1=A(x+2)(x-3)+B(x-1)(x-3)+C(x-1)(x+2);

x=1; -12=A(3)(-2); A=(-12)/(-6)=2

x=-2; 45=B(-3)(-5); B=45/(-15)=-3

x=3; -10=C(2)(5); A=(-10)/10=-1

6.

+2x2 -x3 -3x2 +7x -12 x2 + 3

-2x2 -6x2 2x2 - x - 9

0 -x3 -9x2 +7x -12

+x3 +3x

0 -9x2 +10x -12

+9x2 +27

0 10x +15

7.

+3x4 +2x3 - x2 -x -6 x2 - 1

- 3x4 +3x2 3x2 + 2x +2

0 +2x3 +2x2 - x -6

- 2x3 +2x

0 +2x2 +x -6

- 2x2 +2

0 x -4

8.

+3x3 +2x -4 2x2 + 1

- 3x3 -3/2x 3/2 x

0 + 1/2x -4

9.

+3x3 -5x2 - 4x -8 x2 - 1

- 3x3 + 3/2x2 3/2x2 - 7/4

0 (-7)/2x2 - 4x -8

+7/2x2 - 7/4x

0 - 23/4x -8

10.

2x2 - x -4 7x- 2

-2x2 4/7x 2/7x- 3/49

0 - 3/7x - 4

+3/7x - 6/49

0 - 202/49

11.

X[z]=(2z^3+z)/((z-2)^2 (z-1) )=z(2z^2+1)/((z-2)^2 (z-1) )=A/((z-1) )+B/((z-2) )+C/(z-2)^2

z(2z^2+1)=A*(z-2)^2+B*(z-1)(z-2)+C*(z-1)

z=1; 3=A; A=3;

z=2; 18=C; C=18;

z=0; 0=4A+2B-C; 2B=18-12; B=3

X[z]=3/((z-1) )+3/((z-2) )+18/(z-2)^2

X[z]=(3z^(-1))/((1-z^(-1) ) )+(3z^(-1))/((1-2z^(-1) ) )+(18z^(-2))/(1-2z^(-1) )^2 ; usando la tabla

〖x[n]=3*u[n-1]+3*2〗^([n-1])*u[n-1]+9*n*2^n*u[n]

12.

X[z]=(z+2)/((z-2)*z^2 )=A/(z-2)+B/z+C/z^2

z+2=A*z^2+B(z-2)*z+C(z-2)

z=2; 4=4A; A=1;

z=0; 2=-2C; C=-1;

z=1; 3=A-B-C;

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