Quy đồng mẫu thức ba phân thức Bài 4.1 trang 28 SBT Toán 8 Tập 1

Giải SBT Toán 8 Bài 4: Quy đồng mẫu thức nhiều phân thức

Bài 4.1 trang 28 SBT Toán 8 Tập 1: 

$\begin{array}{l}\frac{x}{x^2-2xy+\text{\hspace{0.17em}}{y}^2-z^2};\frac{y}{y^2-2zy+\text{\hspace{0.17em}}{z}^2-x2}\text{;}\\ \frac{z}{z^2-2zx+\text{\hspace{0.17em}}{x}^2-y^2}\end{array}$

Lời giải:

x² − 2xy + y² − z² = (x − y)² − z² 

= (x – y + z)(x – y − z)

y² – 2yz + z² − x² = (y − z)² − x² 

= (y – z + x)(y – z − x)

= − (x + y – z)(x – y + z)

z² − 2zx + x² − y² = (z − x)² − y² 

= (z – x + y)(z – x − y)

= (x − y – z).(x + y – z)

MTC = (x – y + z)(x + y − z)(x – y − z)

$\begin{array}{l}\frac{x}{x^2-2xy+\text{}{y}^2-z^2}\\ =\frac{x}{(x-y\text{\hspace{0.17em}}+\text{\hspace{0.17em}}z).(x-y-z)}\\ =\frac{x.(x+\text{}y-z)}{(x-y\text{\hspace{0.17em}}+\text{\hspace{0.17em}}z).(x-y-z).(x+\text{\hspace{0.17em}}y-z)};\end{array}$

$\begin{array}{l}\frac{y}{y^2-2zy+\text{}{z}^2-x2}\\ =\frac{-y}{(x-y+\text{\hspace{0.17em}}z).(x+\text{\hspace{0.17em}}y-z)}\\ =\frac{-y.(x-y-z)}{(x-y+\text{\hspace{0.17em}}z).(x+\text{\hspace{0.17em}}y-z)(x-y-z)};\end{array}$

$\begin{array}{l}\frac{z}{z^2-2zx+\text{}{x}^2-y^2}\\ =\frac{z}{(x+\text{\hspace{0.17em}}y-z).(x-y-z)}\\ =\frac{z.(x-y+\text{\hspace{0.17em}}z)}{(x+\text{\hspace{0.17em}}y-z).(x-y-z).(x-y+\text{\hspace{0.17em}}z)}\end{array}$