Представьте в виде рациональной дроби (a/b - b/a) : a-b/3ab = 3a+3b (x-3/x+3 - x^2 + 27/x^2 - 9) * x^2 - 6x + 9/6 = 3-x (3a + 3/a^2-1 - a/a-1) : a-3/1-a = 1

(\frac{a}{b} -\frac{b}{a}) : \frac{a-b}{3ab} =

=(\frac{a^2}{ab} -\frac{b^2}{ab})\cdot \frac{3ab}{a-b} =

=(\frac{a^2 -b^2}{ab})\cdot \frac{3ab}{a-b} =

=\frac{(a-b)(a+b)}{1}\cdot \frac{3}{a-b} =

=3(a+b)=3a+3b

--------------------

(\frac{x-3}{x+3} - \frac{x^2 + 27}{x^2 - 9})\cdot\frac{ x^2 - 6x + 9}{6} =

=(\frac{x-3}{x+3} - \frac{x^2 + 27}{(x-3)(x+3)})\cdot\frac{(x-3)^2}{6} =

=(\frac{(x-3)^2}{(x-3)(x+3)} - \frac{x^2 + 27}{(x-3)(x+3)})\cdot\frac{(x-3)^2}{6} =

=\frac{(x-3)^2 - (x^2 + 27)}{(x-3)(x+3)})\cdot\frac{(x-3)^2}{6} =

=\frac{x^2-6x+9-x^2-27}{x+3})\cdot\frac{x-3}{6} =

=\frac{-6x-18}{x+3})\cdot\frac{x-3}{6} =

=\frac{-6(x+3)}{x+3})\cdot\frac{x-3}{6} =

=-(x-3) =-x+3=3-x

--------------------

(\frac{3a + 3}{a^2-1} - \frac{a}{a-1}) :\frac{ a-3}{1-a} =

=(\frac{3(a+1)}{(a-1)(a+1)} - \frac{a}{a-1}) \cdot\frac{1-a}{ a-3} =

=(\frac{3}{a-1} - \frac{a}{a-1}) \cdot\frac{1-a}{ a-3} =

=\frac{3 -a}{a-1}) \cdot\frac{1-a}{ a-3} =

=\frac{-(a-3)}{-(1-a)}) \cdot\frac{1-a}{ a-3} =

=\frac{-1}{-1}=1