nilai a dan b yang memenuhi kesamaan a/x+2 + b/x-3 =3x+2/x2-x-6 adalah

Kesamaan

a/(x+2) + b/(x-3) = (3x +2)/(x² -x - 6)
.
{a(x-3) + b(x+2)}/(x+2)(x-3) = (3x +2)/(x+2)(x-3)
.
a(x-3) + b(x+2) = 3x + 2
ax - 3a + bx + 2b = 3x + 2
(a+b) x +(-3a+2b) = (3) x + (2)
a+ b = 3
-3a + 2b = 2
.
eliminasikan
a  + b = 3 .........|x2
-3a + 2b = 2
.
2a + 2b = 6
-3a+2b = 2
.....................(-)
5a = 4
a = 4/5

a + b = 3
4/5 + b = 3
b = 3 - 4/5
b = 11/5  = 2¹/₅