ĐKXĐ: \(x\ne y,x\ne z,y\ne z\)
\(\dfrac{4}{\left(y-x\right)\left(z-x\right)}+\dfrac{1}{\left(y-x\right)\left(y-z\right)}+\dfrac{3}{\left(y-z\right)\left(x-z\right)}\)
\(=\dfrac{4\left(y-z\right)}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}-\dfrac{x-z}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}+\dfrac{3\left(x-y\right)}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)
\(=\dfrac{4\left(y-z\right)-\left(x-z\right)+3\left(x-y\right)}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}=\dfrac{2x+y-3z}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)
4(y-z)+z-x+3(y-x)
=4y-4z+z-x+3y-3x
=7y-3z-4x
