Decomposition into partial fractions

Decompose the following functions into partial fractions.

Variant 1
\(\frac{1}{x(x-1)}\)
Result
\(\frac{1}{x-1} - \frac{1}x\)
Variant 2
\( \frac{4}{(x+2)(2x+1)} \)
Result
\(\frac{8}{3(2x+1)} - \frac{4}{3(x+2)}\)
Variant 3
\(\frac{x+1}{x^2 + x - 6}\)
Result
\(\frac{2}{5(x+3)} + \frac{3}{5(x-2)}\)
Variant 4
\(\frac{x^3}{(x-2)^2}\)
Result
\(x + 4 + \frac{12}{(x-2)} + \frac{8}{(x-2)^2}\)
Variant 5
\(\frac{1}{6x^3 - 19x^2 + 2x + 3}\)
Result
\(\frac{9}{50(3x + 1)} + \frac{1}{50(x-3)} - \frac4{25(2x-1)}\)
Variant 6
\(\frac{2x + 5}{x^3 - 6x^2 - 6x - 7}\)
Result
\(\frac{1}{3(x-7)} - \frac{(x+2)}{3(x^2 + x + 1)}\)