\(x^2-4\\ =x^2-2^2\\ =\left(x-2\right)\left(x+2\right)\)

  \(\left(x^2-3x+4\right)\left(-3x+1\right)\)

=\(-3x^3+9x^2-12x\)\(+x^2-3x+4\)

=\(-3x^3+10x^2-15x+4\)

\(\dfrac{2^{12}.3^{10}+2^3.5.2^9.3^9}{2^{12}.3^{12}+2^{12}.3^{12}}\)

\(\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{13}.3^{12}}\)

\(\dfrac{2^{13}.3^{11}.}{2^{13}.3^{12}}\)

\(\dfrac{1}{3}\)

   \(3x^2-3x.(x+1)=9\)

\(\Rightarrow\)\(3x^2-3x^2-3x=9 \)

\(\Rightarrow\)\(-3x=9 \)

\(\Rightarrow x=-3\)

=\(\dfrac{2^{12}.3^5-\left(2^2\right)^6.3^4}{\left(2^2.3\right)^5+2^7.\left(2.3^2\right)^3}\)

=\(\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{10}.3^5+2^7.2^3.3^6}\)

=\(\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{10}.3^5+2^{10}.3^6}\)

=\(\dfrac{2^{12}.2.3^4}{2^{10}.3^5.\left(3+1\right)}\)

=\(\dfrac{2^{13}.3^4}{2^{12}.3^5}\)

=\(\dfrac{2}{3}\)