BÀi 1:
1: \(A=\frac{1}{\left(x-y\right)\left(y-z\right)}+\frac{1}{\left(y-z\right)\left(z-x\right)}+\frac{1}{\left(z-x\right)\left(x-y\right)}\)
\(=\frac{z-x+x-y+y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}=0\)
2: \(B=\frac{4}{\left(y-x\right)\left(z-x\right)}+\frac{3}{\left(y-x\right)\left(y-z\right)}+\frac{3}{\left(y-z\right)\left(x-z\right)}\)
\(=\frac{4}{\left(x-y\right)\left(x-z\right)}-\frac{3}{\left(x-y\right)\left(y-z\right)}+\frac{3}{\left(y-z\right)\left(x-z\right)}\)
\(=\frac{4\left(y-z\right)-3\left(x-z\right)+3\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}=\frac{4y-4z-3x+3z+3x-3y}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}=\frac{y-z}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)
\(=\frac{1}{\left(x-y\right)\left(x-z\right)}\)
Bài 2:
1: \(\frac{1}{x}\cdot\frac{6x}{y}=\frac{6x}{xy}=\frac{6}{y}\)
2: \(\frac{15x}{7y^3}\cdot\frac{2y^2}{x^2}=\frac{15x}{x^2}\cdot\frac{2y^2}{7y^3}=\frac{15}{x}\cdot\frac{2}{7y}=\frac{30}{7xy}\)
3: \(\frac{5x+10}{4x-8}\cdot\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\frac{-2\left(x-2\right)}{x+2}=\frac{5\cdot\left(-2\right)}{4}=-\frac{10}{4}=-\frac52\)
4: \(\frac{x^2-36}{2x+10}\cdot\frac{x^2-25}{x-6}\)
\(=\frac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\frac{\left(x-5\right)\left(x+5\right)}{x-6}=\frac{\left(x+6\right)\left(x-5\right)}{2}\)
5: \(\frac{x^2-9y^2}{x^2y^2}\cdot\frac{3xy}{2x-6y}\)
\(=\frac{\left(x-3y\right)\left(x+3y\right)}{2\left(x-3y\right)}\cdot\frac{3xy}{x^2y^2}\)
\(=\frac{x+3y}{2}\cdot\frac{3}{xy}=\frac{3x+9y}{2xy}\)
6: \(\frac{x+1}{2x+6}\cdot\frac{x+3}{x^2+x}\)
\(=\frac{x+1}{2\left(x+3\right)}\cdot\frac{x+3}{x\left(x+1\right)}=\frac{x+3}{2x}\)
7: \(\frac{3x+5}{x^2-5x}\cdot\frac{x^2-25}{9x^2-25}\)
\(=\frac{3x+5}{x\left(x-5\right)}\cdot\frac{\left(x-5\right)\left(x+5\right)}{\left(3x-5\right)\left(3x+5\right)}=\frac{x+5}{x\left(3x-5\right)}\)
8: \(\frac{x-2}{x+1}\cdot\frac{x^2-2x-3}{x^2-5x+6}\)
\(=\frac{x-2}{x+1}\cdot\frac{\left(x-3\right)\left(x+1\right)}{\left(x-2\right)\left(x-3\right)}=1\)
