a) \(\dfrac{1}{x}-\dfrac{1}{x+1}\)
\(=\dfrac{x+1}{x\left(x+1\right)}-\dfrac{x}{x\left(x+1\right)}\)
\(=\dfrac{x+1-x}{x\left(x+1\right)}\)
\(=\dfrac{1}{x\left(x+1\right)}\left(dpcm\right)\)
b) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
\(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)
\(=\dfrac{y}{xy\left(y-x\right)}-\dfrac{x}{xy\left(y-x\right)}\)
\(=\dfrac{y-x}{xy\left(y-x\right)}\)
\(=\dfrac{1}{xy}\left(dpcm\right)\)
a: \(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{x+1-x}{x\left(x+1\right)}=\dfrac{1}{x\left(x+1\right)}\)
b: \(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)
\(=\dfrac{y-x}{xy\left(y-x\right)}=\dfrac{1}{xy}\)
