__ 9x__^{2} +9x +5

3x-2 ) 27x^{3 }+9x^{2 }-3x-10

__27x__^{3}-18x^{2}

27x^{2}-3x

__27x__^{2}-18x

15x-10

__15x-10__

0

ANSWER: 9x^{2} +9x +5.

The question in the title needs to be clarified to resolve ambiguities in the wording.

A possible interpretation is:

[x^{4}/(x^{3}+7x^{2})]-[(6x+8)/(x-2)],

[x^{2}/(x+7)]-[(6x+8)/(x-2)], (the parentheses clarify the meaning)

(x^{2}(x-2)-(6x+8)(x+7))/((x+7)(x-2)),

(x^{3}-2x^{2}-6x^{2}-50x-56)/((x+7)(x-2)),

(x^{3}-8x^{2}-50x-56)/(x^{2}+5x-14). Now the long algebraic division:

__ x - 13 (quotient)__

x^{2}+5x-14 ) x^{3}-8x^{2} -50x - 56

__x__^{3}+5x^{2}-14x

-13x^{2}-36x - 56

__-13x__^{2}-65x+182

__29x-238__ (remainder)

Several other interpretations are possible.