a) Szorzattá alakítjuk a számlálőt és a nevezőt is:
Számláló: x2 + 7x + 12
D = 72 - 4*1*12 = 49 - 48 = 1 = 12
x1,2 = (-7 ± 1) / 2
x1 = (-7 + 1) / 2 = -6 / 2 = -3
x2 = (-7 - 1) / 2 = -8 / 2 = -4
x2 + 7x + 12 = 1*(x - (-3))*(x - (-4)) = (x + 3)*(x + 4)
Nevező: x2 +2x -8
D = 22 - 4*1*(-8) = 4 + 32 = 36 = 62
x1,2 = (-2 ± 6) / 2
x1 = (-2 + 6) / 2 = 4 / 2 = 2
x2 = (-2 - 6) / 2 = -8 / 2 = -4
x2 + 2x - 8 = 1*(x - 2)*(x - (-4)) = (x - 2)*(x + 4)
A tört: (x + 3)*(x + 4) / (x - 2)*(x + 4) = (x +3) /(x - 2)

b)
Számláló: 3x2 - 13x - 10
D = (-13)2 - 4*3*(-10) = 169 + 120 = 289 = 172
x1,2 = (13 ± 17) / 6
x1 = (13 + 17) / 6 = 30 / 6 = 5
x2 = (13 - 17) / 6 = -4 / 6 = -2/3
3x2 -13x - 10 = 3*(x - 5)*(x - (-2/3)) = (x - 5)*(3x + 2)
Nevező: 2x2 -7x - 15
D = (-7)2 - 4*2*(-15) = 49 + 120 = 169 = 132
x1,2 = (7 ± 13) / 4
x1 = (7 + 13) / 4 = 20 / 4 = 5
x2 = (7 - 13) / 4 = -6 / 4 = -3/2
2x2 -7x - 15 = 2*(x - 5)*(x - (-3/2)) = (x - 5)*(2x + 3)
A tört: (x - 5)*(3x + 2) / (x - 5)*(2x + 3) = (3x +2) /(2x + 3)