a: \(\frac{x}{x-y}=\frac{x\cdot\left(x-y\right)^2}{\left(x-y\right)\left(x-y\right)^2}=\frac{x\left(x-y\right)^2}{\left(x-y\right)^3}\)

\(\frac{y}{\left(x-y\right)^2}=\frac{y\left(x-y\right)}{\left(x-y\right)^2\cdot\left(x-y\right)}=\frac{y\left(x-y\right)}{\left(x-y\right)^3}\)

\(\frac{1}{\left(y-x\right)^3}=\frac{-1}{\left(x-y\right)^3}\)

b: \(\frac{1}{2x+4}=\frac{1}{2\left(x+2\right)}=\frac{1\cdot\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}=\frac{x-2}{2\left(x+2\right)\left(x-2\right)}\)

\(\frac{x}{2x-4}=\frac{x}{2\left(x-2\right)}=\frac{x\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}\)

\(\frac{3}{4-x^2}=\frac{-3}{x^2-4}=\frac{-3}{\left(x-2\right)\left(x+2\right)}=\frac{-3\cdot2}{2\left(x-2\right)\left(x+2\right)}=\frac{-6}{2\left(x-2\right)\left(x+2\right)}\)

a: \(\frac{x}{x-y}=\frac{x\cdot\left(x-y\right)^2}{\left(x-y\right)\left(x-y\right)^2}=\frac{x\left(x-y\right)^2}{\left(x-y\right)^3}\)

\(\frac{y}{\left(x-y\right)^2}=\frac{y\left(x-y\right)}{\left(x-y\right)^2\cdot\left(x-y\right)}=\frac{y\left(x-y\right)}{\left(x-y\right)^3}\)

\(\frac{1}{\left(y-x\right)^3}=\frac{-1}{\left(x-y\right)^3}\)

b: \(\frac{1}{2x+4}=\frac{1}{2\left(x+2\right)}=\frac{1\cdot\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}=\frac{x-2}{2\left(x+2\right)\left(x-2\right)}\)

\(\frac{x}{2x-4}=\frac{x}{2\left(x-2\right)}=\frac{x\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}\)

\(\frac{3}{4-x^2}=\frac{-3}{x^2-4}=\frac{-3}{\left(x-2\right)\left(x+2\right)}=\frac{-3\cdot2}{2\left(x-2\right)\left(x+2\right)}=\frac{-6}{2\left(x-2\right)\left(x+2\right)}\)

\(\dfrac{x+1}{4x^2y}=\dfrac{3y\left(x+1\right)}{12x^2y^2}\)

\(\dfrac{y-2}{6xy^2}=\dfrac{2x\left(y-2\right)}{12x^2y^2}\)

MT1: x – y

MT2: 1

MTC: x – y

NTP1: 1;    NTP2: x – y.

Quy đồng: 

a: \(\frac{x+y}{x^2\left(y+z\right)}=\frac{\left(x+y\right)\cdot y^2z^2\left(x+z\right)\left(x+y\right)}{x^2y^2z^2\left(x+y\right)\left(y+z\right)\left(x+z\right)}=\frac{\left(x+z\right)\cdot y^2z^2\left(x+y\right)^2}{x^2y^2z^2\left(x+y\right)\left(y+z\right)\left(x+z\right)}\)

\(\frac{y+z}{y^2\left(x+z\right)}=\frac{\left(y+z\right)\cdot x^2z^2\left(x+y\right)\left(y+z\right)}{x^2y^2z^2\left(x+y\right)\left(y+z\right)\left(x+z\right)}=\frac{x^2z^2\left(y+z\right)^2\cdot\left(x+y\right)}{x^2y^2z^2\left(x+y\right)\left(y+z\right)\left(x+z\right)}\)

\(\frac{z+x}{z^2\left(x+y\right)}=\frac{\left(z+x\right)\cdot x^2y^2\cdot\left(x+z\right)\left(y+z\right)}{x^2y^2z^2\left(x+y\right)\left(x+z\right)\left(y+z\right)}=\frac{x^2y^2\left(x+z\right)^2\cdot\left(y+z\right)}{x^2y^2z^2\left(x+y\right)\left(y+z\right)\left(x+z\right)}\)

b: \(\frac{5x}{x^2+5x+6}=\frac{5x}{\left(x+2\right)\left(x+3\right)}=\frac{5x\left(x+5\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)

\(\frac{2x+3}{x^2+7x+10}=\frac{2x+3}{\left(x+2\right)\left(x+5\right)}=\frac{\left(2x+3\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)

\(-5=\frac{-5\left(x+2\right)\left(x+3\right)\left(x+5\right)}{\left(x+2\right)\left(x+3\right)\left(x+5\right)}\)

\(\dfrac{1}{3x+xy}=\dfrac{1}{x\left(y+3\right)}=\dfrac{\left(x+y\right)^2}{x\left(y+3\right)\left(x+y\right)^2}\)

\(2x+2y=2\left(x+y\right)=\dfrac{2\left(x+y\right)\cdot x\left(y+3\right)\left(x+y\right)^2}{x\left(y+3\right)\left(x+y\right)^2}\)

\(\dfrac{1}{x^2+2xy+y^2}=\dfrac{3x+xy}{x\left(y+3\right)\left(x+y\right)^2}\)

a: 1/x^2y=1/x^2y

3/xy=3x/x^2y

b: \(\dfrac{x}{x^2+2xy+y^2}=\dfrac{x}{\left(x+y\right)^2}\)

\(\dfrac{2x}{x^2+xy}=\dfrac{2}{x+y}=\dfrac{2x+2y}{\left(x+y\right)^2}\)