Divide:

x² + 3x - 54 by x - 6

(x² + 3x - 54) ÷ (x - 6)

= (x² + 9x - 6x - 54) ÷ (x - 6)

= [x(x + 9) - 6(x + 9)] ÷ (x - 6)

= [(x + 9)(x - 6)] ÷ (x - 6)

= $\dfrac{(x + 9)\cancel{(x - 6)}}{\cancel{(x - 6)}}$

= (x + 9)

Hence, (x² + 3x - 54) ÷ (x - 6) = x + 9