BT1:
a) \(\dfrac{-20x}{3y^2}:\left(\dfrac{-4x^3}{5y}\right)\)
\(=\dfrac{-20x}{3y^2}\cdot\dfrac{5y}{-4x^3}\)
\(=\dfrac{-20x\cdot5y}{3y^2\cdot-4x^3}\)
\(=\dfrac{5\cdot5}{3y\cdot x^2}=\dfrac{25}{3x^2y}\)
b) \(\dfrac{4x+12}{\left(x+4\right)^2}:\dfrac{3\left(x+3\right)}{x+4}\)
\(=\dfrac{4\left(x+3\right)}{\left(x+4\right)^2}\cdot\dfrac{x+4}{3\left(x+3\right)}\)
\(=\dfrac{4\left(x+3\right)\cdot\left(x+4\right)}{\left(x+4\right)^2\cdot3\left(x+3\right)}\)
\(=\dfrac{4}{3\left(x+4\right)}\)
3:
a: \(P:\dfrac{4x^2-16}{2x+1}=\dfrac{4x^2+4x+1}{x-2}\)
=>\(P=\dfrac{\left(2x+1\right)^2}{x-2}\cdot\dfrac{4\left(x^2-4\right)}{2x+1}=4\left(x+2\right)\left(2x+1\right)\)
b: \(\dfrac{2x^2+4x+8}{x^3-3x^2-x+3}:P=\dfrac{x^3-8}{\left(x+1\right)\left(x-3\right)}\)
=>\(P=\dfrac{2\left(x^2+2x+4\right)}{\left(x-3\right)\left(x^2-1\right)}:\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{\left(x+1\right)\left(x-3\right)}\)
\(=\dfrac{2\left(x^2+2x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)}\cdot\dfrac{\left(x+1\right)\left(x-3\right)}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\dfrac{2}{x-1}\)
