Resposta:

a = 15

Explicação passo a passo:

[tex]\displaystyle \frac{120x^2+29x-65}{ax-2} =8x+3-\frac{59}{ax-2} \\\\\\ \frac{120x^2+29x-65}{ax-2} =\frac{(8x+3)(ax-2)-59}{ax-2}\\\\\\120x^2+29x-65=8ax^2-16x+3ax-6-59\\\\120x^2+29x-65=8ax^2+(3a-16)x-65[/tex]

Comparando as expressões:

120 = 8a => a =120/8 = 15

3a - 16 = 29 => 3a = 29 + 16 => a = 45/3 = 15