Question

A =  ( x²y +xy ) / x²y -y ) 

B = -2x² / x³  - x

a) Rút gọn các phân thức

b) Tính tổng A + B 

mọi người giúp mik nha

 

Answer 1

a) Ta có:\(A=\frac{x^2y+xy}{x^2y-y}=\frac{xy\left(x+1\right)}{y\left(x^2-1\right)}=\frac{x+1}{\left(x+1\right)\left(x+1\right)}=\frac{1}{x-1}\)

\(B=\frac{-2x^2}{x^3-x}=\frac{-2x^2}{x\left(x^2-1\right)}=\frac{-2x}{\left(x+1\right)\left(x-1\right)}\)

b) \(A+B=\frac{1}{x-1}+\frac{-2x}{\left(x+1\right)\left(x-1\right)}=\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{-2x}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{x+1-2x}{\left(x+1\right)\left(x-1\right)}=\frac{-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=-\frac{1}{x+1}\)