Divide:

12x² + 7xy - 12y² by 3x + 4y

(12x² + 7xy - 12y²) ÷ (3x + 4y)

= (12x² + 16xy - 9xy - 12y²) ÷ (3x + 4y)

= [4x(3x + 4y) - 3y(3x + 4y)] ÷ (3x + 4y)

= [(3x + 4y)(4x - 3y)] ÷ (3x + 4y)

= $\dfrac{[\cancel{(3x + 4y)}(4x - 3y)]}{\cancel{(3x + 4y)}}$

= 4x - 3y

Hence, (12x² + 7xy - 12y²) ÷ (3x + 4y) = (4x - 3y)