Question

Tìm m để:

a, \(\dfrac{x-m}{x-1}+\dfrac{x-2}{x+1}=2\) vô nghiệm

b, \(\dfrac{x+1}{x-1}=\dfrac{x+2}{x-m}\) có nghiệm duy nhất

Answer 1

a: ĐKXĐ: x<>1; x<>-1

\(\Leftrightarrow\left(x-m\right)\left(x+1\right)+\left(x-2\right)\left(x-1\right)=2\left(x^2-1\right)\)

\(\Leftrightarrow x^2+x-mx-m+x^2-3x+2-2x^2+2=0\)

\(\Leftrightarrow-2x-mx-m+4=0\)

=>x(-m-2)=m-4

Để PT VN thì -m-2=0

=>m=-2

b: ĐKXĐ: x<>1; x<>m

\(\Leftrightarrow\left(x+1\right)\left(x-m\right)=\left(x+2\right)\left(x-1\right)\)

=>x^2-xm+x-m=x^2+x-2

=>-xm+x-m=x+2

=>-xm-m=2

=>-xm=m+2

=>xm=-m-2

Để PT có nghiệm duy nhất thì m<>0