Verified answer

[tex] \frac{6}{3x - 11} - \frac{8}{7x + 2} = \frac{3x - 20}{21 {x}^{2} - 71x - 22} \\ \frac{6(7x + 2) - 8(3x - 11)}{(3x - 11)(7x + 2)} = \frac{3x - 20}{21 {x}^{2} - 71x - 22} \\ \frac{42x + 12 - 24x + 88}{21 {x}^{2} + 6x - 77x - 22} = \frac{3x - 20}{21 {x}^{2} - 71x - 22} \\ \frac{18x + 100 }{21 {x}^{2} - 71x - 22} = \frac{3x - 20}{21 {x}^{2} - 71x - 22} \\ (18x + 100)(21 {x}^{2} - 71x - 22) = (21 {x}^{2} - 71x - 22)(3x - 20)[/tex]

[tex]18x + 100 = 3x - 20 \\ 15x = - 120 \\ x = \frac{ - 120}{15} \\ x = - 8[/tex]