Matematicas

Descomponer en fracciones parciales

1. -x+24x2-x-12 =A (X-4) + B(X+3)

-x+24x2-x-12 =A x+3+B(X-4)(X-4)
-X+24 =A(X+3)+ B(X-4)(-3)
3 +24 = A(0) + B(-7)
27/7 = B
-X+24 =A(X+3)+ B(X-4) (4)
-4 +24 = A(7) + B(0)20 = 7A
20/7 =A
-x+24x2-x-12 =20 7(X-4) + 277(X+3)

2. –X-31X2+3X-18 = A(X+6) +B(X-3)

–X-31X2+3X-18 = AX-3+ B(X+6)X+6(X+3)-X-31=A(X-3)+B(X+6) si X = (3)
-3 -31 = A(0) + B(9)
-34 =9B
B= -34/9-X-31=A(X-3)+B(X+6) (-6)
-25 = -9A + B(0)
A= -25/9

–X-31X2+3X-18 = -259(X+6) +-349(X-3)

3. 5x-15x2-x-12 = AX-4 + BX+35x-15x2-x-12 = AX+3+B(X-4)X-4(X+3)

5X-15= A(X+3)+B(X-4) si X= 4
20-15= 7A+B(0)
5=7A
A=5/7

5X-15= A(X+3)+B(X-4) si X= -3
-30= A(0) + B(-7)
-30/-7=B
B=30/7

5x-15x2-x-12 = 57X-4 + 307X+3

4. 13X-13X2- 12X-28 = A(X-14)+B(X+2)

13X-13X-14(X+2) = A(X+2)(X-14)+B(X-14)(X+2)

13X-13= A(X+2) + B(X – 14)si X = 14
182-13 = -12A +B(0)
169 = -12A
A= -169/12

13X-13= A(X+2) + B(X – 14) si X = -2
-26-13 = A(0) + B(-16)
-39= -16B
B= 39/16

13X-13X2-12X-28 = -16912(X-14)+3916(X+2)

5. X2+ X-12X2-10X+24= A(X-6)+B(X-4)

* X2+ X-12(X-6)(X-4)= AX-4+ B(X-6)(X-6)(X-4)

X2+X-12= A(X-4)+B(X-6) si X=4
14+4-12= A(0) + B(-10)
6= -10B
B=-6/10

X2+X-12= A(X-4)+B(X-6) si X= 6
36+6-12= A(2) +B(0)
30=2A
A= 15

X2+ X-12X2-10X+24= 15(X-6)+-610(X-4)