Factor

6x^2+x-2 / 3x^2+14x+8

Split the second term in 6x^2 + x - 2 into two terms

6x^3 + 4x - 3x - 2/3x^2 + 14x + 8

Factor out the common terms in the first two term, then in the last two terms

2x (3x + 2) - (3x + 2) / 3x^2 + 14x + 8

Factor out the common term 3x + 2

(3x + 2) (2x - 1) / 3x^2 + 14x + 8

Split the second term in 3x^2 + 14x + 8 into two terms

(3x + 2) (2x - 1) / 3x^2 + 12x + 2x + 8

Factor out common terms in the first two terms, then in the last two terms

(3x + 2) (2x - 1) / 3x (x + 4) + 2 (x + 4)

Factor out the common term x + 4

(3x + 2) (2x - 1) / (x + 4) (3x + 2)

Cancel 3x + 2

2x - 1/x + 4