Ditentukan kesamaan pecahan: m/x+1 + n/n+2 kongruen dengan 6x+2/x^2+3x+2 hitunglah nilai m dan n?

Kesamaan Pecahan

m/(x+1) + n/(x+2) = (6x+2)/(x² +3x+2)
.
ruas kiri
m(x+1) + n(x+2) =..sama kan penyebutkan
= {m(x+2)+ n(x+1)} /(x+1)(x+2)
= (mx + 2m + nx +n)/(x²+3x+2)
= {(m+n)x + (2m+n)} / (x² + 3x + 2)
ruas kiri = ruas kanan
{(m+n)x + (2m+n)}/(x²+3x+2) = (6x+2) / (x²+3x+2)
maka
(m+n) x + (2m+n) = (6)x + (2)
.
m+n = 6
2m+n = 2
------------(-)
- m = 4 --> m = - 4

m+ n = 6--> n = 6 - m
n = 6 - (-4)
n = 6 + 4
n = 10

(m,n) = (-4, 10)