If $t = \frac{(2-x)(3-x)}{3x^2 -7x + 6 }$, then find $\frac{-x^4 + 2x^3 - 3x^2 + 2x}{3x^2 -7x + 6 }$? Suppose that $t =\frac{(2-x)(3-x)}{3x^2 -7x + 6 }$.  Can you, please, give me any hints to express the following in terms of $t$:
$$\frac{-x^4 + 2x^3 - 3x^2 + 2x}{3x^2 -7x + 6 }?$$

1-Firstly, expand numerator of the given equation like
$$t=\frac{x^2-5x+6}{3x^2-7x+6}$$
2-Don't do anything with the denominator because denominator is same in the required answer.
3-Multiply $t$ by $-x^2$, to get $-x^4 $ term.
4-Then, make the same terms which you required by adding and subtracting terms.
5-At the end, you have$$-x^2t+\frac{-3x^3+3x^2+2x}{3x^2-7x+6}=\frac{-x^4+2x^3-3x^2+2x}{3x^2-7x+6}$$
