i am guessing it is (t^3-t)/(t^3+5t^2-6t), use parantheses to make yourself clear. The way you wrote it is t^3 - t/(t^3) +5t^2 - 6t. which would be t^3 - 1/t^2 + 5t^2 - 6t
but your answer is trickier.
the top factors to t(t^2-1), further to t(t+1)(t-1)
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i am guessing it is (t^3-t)/(t^3+5t^2-6t), use parantheses to make yourself clear. The way you wrote it is t^3 - t/(t^3) +5t^2 - 6t. which would be t^3 - 1/t^2 + 5t^2 - 6t
but your answer is trickier.
the top factors to t(t^2-1), further to t(t+1)(t-1)
the bottom factors to t(t+6)(t-1)
the t, and the (t-1) cancel
the result is (t+1)/(t+6)