Vd7:
a: \(\dfrac{1}{xy^3}=\dfrac{1\cdot x}{x^2y^3}=\dfrac{x}{x^2y^3}\)
\(\dfrac{2}{x^2y}=\dfrac{2\cdot y^2}{x^2y\cdot y^2}=\dfrac{2y^2}{x^2y^3}\)
b: \(\dfrac{1}{x^2-2x}=\dfrac{1}{x\left(x-2\right)}\)
\(\dfrac{2}{x}=\dfrac{2\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2x-4}{x\left(x-2\right)}\)
c: \(\dfrac{x}{x^2-9}=\dfrac{x}{\left(x-3\right)\left(x+3\right)}\)
\(\dfrac{x}{x-3}=\dfrac{x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2+3x}{\left(x-3\right)\left(x+3\right)}\)
d: \(\dfrac{2}{x^2-x-6}=\dfrac{2}{\left(x-3\right)\left(x+2\right)}\)
\(\dfrac{3}{x+2}=\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}=\dfrac{3x-9}{\left(x-3\right)\left(x+2\right)}\)
e: \(\dfrac{4x}{x^2-x-6}=\dfrac{4x}{\left(x-3\right)\left(x+2\right)}=\dfrac{4x\cdot x}{x\left(x-3\right)\left(x+2\right)}=\dfrac{4x^2}{x\left(x-3\right)\left(x+2\right)}\)
\(\dfrac{1}{x^2+2x}=\dfrac{1}{x\left(x+2\right)}=\dfrac{\left(x-3\right)}{x\left(x+2\right)\left(x-3\right)}\)
Vd4:
a: \(\dfrac{2\left(x+1\right)^2}{4x\left(x+1\right)}\)
\(=\dfrac{2\left(x+1\right)^2:2\left(x+1\right)}{4x\left(x+1\right):2\left(x+1\right)}\)
\(=\dfrac{x+1}{2x}\)
b: \(\dfrac{\left(8-x\right)\left(-x-2\right)}{\left(x+2\right)^2}\)
\(=\dfrac{\left(x-8\right)\left(x+2\right)}{\left(x+2\right)^2}\)
\(=\dfrac{x-8}{x+2}\)
c: \(\dfrac{2\left(x-y\right)}{y-x}=\dfrac{2\left(x-y\right)}{-\left(x-y\right)}=-2\)
