g) \(\dfrac{7x^2-7x^3}{x^3-3x^2+3x-1}\)
\(=\dfrac{7x^2\left(1-x\right)}{\left(x-1\right)^3}\)
\(=\dfrac{-7x^2\left(x-1\right)}{\left(x-1\right)^3}\)
\(=\dfrac{-7x^2}{\left(x-1\right)^2}\)
\(=\dfrac{-7x^2}{x^2-2x+1}\)
h) \(\dfrac{x^2-6x+9}{4x^2-12x}\)
\(=\dfrac{\left(x-3\right)^2}{4x\left(x-3\right)}\)
\(=\dfrac{x-3}{4x}\)
i) \(\dfrac{3x^3-3x}{x^3-1}\)
\(=\dfrac{3x\left(x^2-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{3x\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{3x\left(x+1\right)}{x^2+x+1}\)
\(=\dfrac{3x^2+3x}{x^2+x+1}\)
j) \(\dfrac{x^3+3x^2+3x+1}{4x^3+4x^2}\)
\(=\dfrac{\left(x+1\right)^3}{4x^2\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)^2}{4x^2}\)
\(=\dfrac{x^2+2x+1}{4x^2}\)
h) \(\dfrac{10x^2y+2xy^2}{2xy}\)
\(=\dfrac{2xy\left(5x+y\right)}{2xy}\)
\(=5x+y\)
