# Phân thức đại số

4/(y-x)(x-z)+3/(y-x)(y-z)+3/(y-z)(x-z)

27 tháng 2 2020 lúc 19:51

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

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

$=\frac{4y-4z+3x-3z+3y-3x}{\left(y-x\right)\left(y-z\right)\left(x-z\right)}=\frac{7y-7z}{\left(y-x\right)\left(y-z\right)\left(x-z\right)}$

$=\frac{7\left(y-z\right)}{\left(y-x\right)\left(y-z\right)\left(x-z\right)}=\frac{7}{\left(y-x\right)\left(x-z\right)}$

$=\frac{7}{yx-yz-x^2+xz}$

Bình luận (0)
27 tháng 2 2020 lúc 19:36

$=\frac{4\left(y-z\right)+3\left(x-z\right)+3\left(y-x\right)}{\left(y-x\right)\left(y-z\right)\left(x-z\right)}=\frac{7\left(y-z\right)}{\left(y-x\right)\left(y-z\right)\left(x-z\right)}=\frac{7}{\left(y-x\right)\left(x-z\right)}$

Bình luận (0)

Các câu hỏi tương tự