Question

\(\dfrac{4}{(y-x)(z-x)}+\dfrac{3}{(y-x)(y-z)}+\dfrac{3}{(y-z)(x-z)}\)

Answer 1

Ta có: \(\dfrac{4}{\left(y-x\right)\left(z-x\right)}+\dfrac{3}{\left(y-x\right)\left(y-z\right)}+\dfrac{3}{\left(y-z\right)\left(x-z\right)}\)

\(=\dfrac{4\left(y-z\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}+\dfrac{3\left(x-z\right)}{\left(x-y\right)\left(y-z\right)\left(x-z\right)}+\dfrac{3\left(x-y\right)}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)

\(=\dfrac{4y-4z+3x-3z+3x-3y}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)

\(=\dfrac{6x+y-7z}{\left(x-y\right)\left(x-z\right)\left(y-z\right)}\)